## MAT-301 History of Mathematics

This course surveys the historical development of mathematics. Mathematical pedagogy, concepts, critical thinking, and problem solving are studied from a historical perspective. The course aims at serving the needs of a wide student audience as well as connecting the history of mathematics to other fields such as the sciences, engineering, economics, and social sciences. The course explores the major themes in mathematics history: arithmetic, algebra, geometry, trigonometry, calculus, probability, statistics, and advanced mathematics. The historical development of these themes is studied in the context of various civilizations ranging from Babylonia and Egypt through Greece, the Far and Middle East, and on to modern Europe. Topics covered include ancient mathematics, medieval mathematics, early modern mathematics, and modern mathematics.

Advisory: It is advisable to have knowledge equivalent to MAT 231: Calculus I in order to succeed in this course. Students are responsible for making sure they have this knowledge. This course will not fulfill the Higher Level Math requirement with the ASAST/BSAST degree programs.

#### Study Methods- :

Preview the Online Syllabus />*(Please visit the University bookstore to view the correct materials for each course by semester as the contents of the actual online syllabus may differ from the preview due to updates or revisions)*

## Topics covered

Analysis of the elementary real functions: algebraic, trigonometric, exponentials and their inverses and composites. Their graphs and derivatives. Topics include limits, continuity, asymptotes, the definition of the derivative, derivatives and derivative rules for algebraic, trigonometric, exponentials, and logarithms. Implicit differentiation, related rates, linear approximation, differentials, mean value theorem, maxima and minima, curve sketching, l’Hospital’s rule.

### Calculus I Course Overview

- MATH 1020 is a four-credit calculus course that focuses on single variable calculus through graphical, analytical, and numerical techniques. Differentiation and its applications are thoroughly discussed. Basic integration techniques are introduced. Mathematical manipulation and computational competence is equally weighted with the ability to analyze, evaluate, synthesize and form accurate decisions using relevant information in applied settings.

*** This course is considered an upper-level undergraduate course (300 level or above)**

### Calculus I Course Outcomes

- Apply the core concepts of differential and integral calculus to solve problems in Calculus 1:
- Limits and Continuity: Graphical interpretation, numerical approximation, limit laws, Squeeze Theorem, Intermediate Value Theorem, tangent and velocity problems, L’Hopital’s rule
- Derivatives: Formal definition of a derivative, Delta – Epsilon proofs, differentiation rules, trig formulas, chain, product and quotient rules, implicit and logarithmic differentiation
- Applications of the derivative: Rates of change, related rates, Mean Value Theorem. curve sketching, local and absolute extrema, optimization, linear approximations, Newton’s method.
- Integrals: Approximating areas, antidifferentiation, Riemann sums, Fundamental Theorem of Calculus, definite and indefinite integrals, substitution methods
- Applications of Integration: Area under and between curves, volumes of revolutions, arc length, work, hydrostatic force, moments and centers of mass, exponential growth and decay models, hyperbolic functions

### Calculus I Course Prerequisites

*Please note these prerequisites are highly suggested and support course preparedness and success. We recommend having completed the listed prerequisites before enrolling and within the past seven years.

### How do exams work?

All exams are taken online. Major exams are required to be proctored online through ProctorU. For instructions on how to take your exams online, visit UNE Online’s ProctorU site. Please note exams must also be proctored with the UNE-approved external webcam.

### How do labs work?

### MATH 1020: Lecture

- Credits: 4
- Tuition: $1,480
- Registration: $30
**Total:**$1,510 (Total payment is due in full at the time of registration)

*The cost of the materials is not included in this total

### Required course materials

**Mandatory External Webcam and Whiteboard for Proctored Exams**- SPHP courses require the use of the UNE-approved external webcam for all proctored exams.The UNE-approved whiteboard is optional dependent on the course.(Webcam & Whiteboard Ordering Information)

*Herman, E., & Strang, G. Calculus volume 1: CCBY-NC-SA 4.0*

- MATH 1020 is a lecture-only course. We do not offer a lab component and therefore no lab materials are needing to be purchased.

**Complete at Your Own Pace within 16 weeks****24/7 Online Registration****Courses Typically Begin Every Two to Three Weeks**Working at the pace typical for a four-semester hour course, the average student will complete this online course in approximately 16 weeks. Many students have elected an online course for the sake of flexibility. Since the course is self-paced, you may be able to complete the course in less than 16 weeks.

You may enroll for a course at any time through our self-service registration portal. Payment is needed in full at the time of registration.

You must be registered for your class by 12:00 noon EST the Monday before the class starts. Your official start date is the date that the course opens and you will have 16 weeks from that date to complete your course.

### Your Dedicated Student Support Specialists

If you have any questions about registration, the coursework or course requirements, please reach out to one of our student service advisors at the email or phone number below.

*If you intend to use VA Benefits or Military Tuition Assistance, please do not use the self-registration portal. Please call (855) 325-0894 to be directed to the appropriate office for assistance or view our Veteran Benefits page for more info.*

## Programme Structure

### Level 100

### Level 200

### First Semester

This course aims to provide a first approach to the subject of algebra, which is one of the basic pillars of modern mathematics. The focus of the course will be the study of certain structures called groups, rings, fields and some related structures. Abstract algebra gives to student a good mathematical maturity and enable learners to build mathematical thinking and skill. The topics to be covered are injective, subjective and objective mappings. Product of mappings, inverse of a mapping. Binary operations on a set. Properties of binary operations (commutative, associative and distributive properties). Identity element of a set and inverse of an element with respect to a binary operation. Relations on a set. Equivalence relations, equivalence classes. Partition of set induced by an equivalence relation on the set. Partial and total order relations on a set. Well-ordered sets. Natural numbers mathematical induction. Sum of the powers of natural numbers and allied series. Integers divisors, primes, greatest common divisor, relatively prime integers, the division algorithm, congruencies, the algebra of residue classes. Rational and irrational numbers. Least upper bound and greatest lower bound of a bounded set of real numbers. Algebraic structures with one or two binary operations. Definition, examples and simple properties of groups, rings, integral domains and fields.

This course is designed to develop advanced topics of differential and integral calculus. Emphasis is placed on the applications of definite integrals, techniques of integration, indeterminate forms, improper integrals and functions of several variables. The topics to be covered are differentiation of inverse, circular, exponential, logarithmic, hyperbolic and inverse hyperbolic functions. Leibnitz’s theorem. Application of differentiation to stationary points, asymptotes, graph sketching, differentials, L’Hospital rule. Integration by substitution, by parts and by use of partial fractions. Reduction formulae. Applications of integration to plane areas, volumes and surfaces of revolution, arc length and moments of inertia. Functions of several variables, partial derivatives.

### Second Semester

The construction of mathematical models to address real-world problems has been one of the most important aspects of each of the branches of science. It is often the case that these mathematical models are formulated in terms of equations involving functions as well as their derivatives. Such equations are called differential equations. If only one independent variable is involved, often time, the equations are called ordinary differential equations. The course will demonstrate the usefulness of ordinary differential equations for modeling physical and other phenomena. Complementary mathematical approaches for their solution will be presented. The topics to be covered are vector algebra with applications to three-dimensional geometry. First order differential equations applications to integral curves and orthogonal trajectories. Ordinary linear differential equations with constant coefficients and equation reducible to this type. Simultaneous linear differential equations. Introduction to partial differential equations.

This course is designed to give an introduction to complex numbers and matrix algebra, which are very important in science and technology, as well as mathematics. The topics to be covered are complex numbers and algebra of complex numbers. Argand diagram, modulus-argument form of a complex number. Trigonometric and exponential forms of a complex number. De Moivre’s theorem, roots of unity, roots of a general complex number, nth roots of a complex number. Complex conjugate roots of a polynomial equation with real coefficients. Geometrical applications, loci in the complex plane. Transformation from the z-plane to the w-plane. Matrices and algebra of matrices and determinants, Operations on matrices up to . inverse of a matrix and its applications in solving systems of equation. Gauss-Jordan method of solving systems of equations. Determinants and their use in solving systems of linear equations. Linear transformations and matrix representation of linear transformations.

### Level 300

### First Semester

This course covers the fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, and the interchange of limit operations. It shows the utility of abstract concepts and teaches an understanding and construction of proofs. The topics to be covered include

limit of a sequence of real numbers, standard theorems on limits, bounded and monotonic sequences of real numbers, infinite series of real numbers, tests for convergence, power series, limit, continuity and differentiability of functions of one variable, Rolle’s theorem, mean value theorems, Taylor’s theorem, definition and simple properties of the Riemann integral.

This course introduces more algebraic methods needed to understand real world questions. It develops fundamental algebraic tools involving matrices and vectors to study linear systems of equations and Gaussian elimination, linear transformations, orthogonal projection, least squares, determinants, eigenvalues and eigenvectors and their applications. The topics to be covered are axioms for vector spaces over the field of real and complex numbers. Subspaces, linear independence, bases and dimension. Row space, Column space, Null space, Rank and Nullity. Inner Products Spaces. Inner products, Angle and Orthogonality in Inner Product Spaces, Orthogonal Bases, Gram-Schmidt orthogonalization process. Best Approximation. Eigenvalues and Eigenvectors. Diagonalization. Linear transformation, Kernel and range of a linear transformation. Matrices of Linear Transformations.

This course provides an introduction to basic computer programming concepts and techniques useful for Scientists, Mathematicians and Engineers. The course exposes students to practical applications of computing and commonly used tools within these domains. It introduces techniques for problem solving, program design and algorithm development. MATLAB (approximately 24 lectures): Basic programming: introduction to the MATLAB environment and the MATLAB help system, data types and scalar variables, arithmetic and mathematical functions, input and output, selection and iteration statements. Functions: user defined functions, function files, passing information to and from functions, function design and program decomposition, recursion. Arrays: vectors, arrays and matrices, array addressing, vector, matrix and element-by-element operations. Graphics: 2-D and 3-D plotting. Other topics to be covered are coding in a High Level Language using MATLAB/OCTAVE. At least one Computer Algebra System (CAS): MAPLE, MAXIMA MATHEMATICA, DERIVE will also be covered.

Limit and continuity of functions of several variables partial derivatives, differentials, composite, homogenous and implicit functions Jacobians, orthogonal curvilinear coordinates multiple integral, transformation of multiple integrals Mean value and Taylor’s Theorems for several variables maxima and minima with applications.

### Second Semester

**This course covers vector valued functions. It introduces students to the concept of change and motion and the manner in which quantities approach other quantities. Topics include limits, continuity, derivatives of vector functions, gradient, divergence, curl, formulae involving gradient, divergence, laplacian, orthogonal curvilinear coordinates, line integrals, Green’s theorem in the plane, surface integrals. Other topics are the divergence theorem, improper integrals, Gamma functions, Beta functions, the Riemann Stieltjes Integral, pointwise and uniform convergence of sequence and series, integration and differentiation term by term.**Limits, continuity and derivatives of vector functions gradient, divergence and curl formulae involving gradient, divergence, curl and laplacian and orthogonal curvilinear coordinates line integrals Green’s theorem in the plane surface integrals the divergence theorem improper integrals Gamma and Beta functions The Riemann Stieltjes integral pointwise and uniform convergence of sequence and series integration and differentiation term by term.

This course introduces more algebraic methods needed to understand real world questions. It develops fundamental algebraic tools involving direct sum of subspaces, complement of subspace in a vector space and dimension of the sum of two subspaces. Other topics to be covered are one-to one, onto and bijective linear transformations, isomorphism of vector spaces, matrix of a linear transformation relative to a basis, orthogonal transformations, rotations and reflections, real quadratic forms, and positive definite forms.

This course is designed to introduce students to basic concepts in mathematical modelling. It also equips the students with mathematical modelling skills with emphasis on using mathematical models to solve real- life problems. Topics to be covered in this course includes: methodology of model building, problem identification and definition, model formulation and solution, consideration of varieties of models involving equations like algebraic, ordinary differential equation, partial differential equation, difference equation, integral and functional equations, Single species models (exponential, logistic and, the Gompertz growth models), interacting species models: (predator-prey models, competing species models, cooperating species models, multi-species models), the SI, SIR, SIS, SIRS and SEIR epidemic models, the basic reproduction number R0: derivation, interpretation and application to stability analysis of disease-free and endemic equilibria, and case studies: Malaria, HIV-AIDS, TB.

This course focuses on traditional algebra topics that have found greatest application in science and engineering as well as in mathematics. The topics to be covered are: axioms for groups with examples, subgroups, simple properties of groups, cyclic groups, homomorphism and isomorphism, axioms for rings, and fields, with examples, simple properties of rings, cosets and index of a subgroup, Lagrange’s theorem, normal subgroups and quotient groups, the residual class ring, homomorphism and isomorphism of rings, subrings.

### Level 400

### First Semester

This course is designed as a basic introductory course in the analysis of metric spaces. It is aimed at providing the abstract analysis components for the degree course of a student majoring in mathematics. This course affords students an opportunity to gain some familiarity with the axiomatic method in analysis. The topics to be covered are: metric spaces, open spheres, open sets, limit points, closed sets, interior, closure, boundary of a set, sequences in metric spaces, subsequences, upper and lower limits of real sequences, continuous functions on metric spaces, uniform continuity, isometry, homomorphism, complete metric spaces, compact sets in a metric space, Heine-Borel theorem, connected set, and the inter-mediate value theorem.

The construction of mathematical models to address real-world problems has been one of the most important aspects of each of the branches of science. It is often the case that these mathematical models are formulated in terms of equations involving functions as well as their derivatives. Such equations are called differential equations. If only one independent variable is involved, often time, the equations are called ordinary differential equations. The course will demonstrate the usefulness of ordinary differential equations for modelling physical and other phenomena. Complementary mathematical approaches for their solution will be presented. Topics covered include linear differential equation of order n with coefficients continuous on some interval J, existence-uniqueness theorem for linear equations of order n, determination of a particular solution of non-homogeneous equations by the method of variation of parameters, Wronskian matrix of n independent solutions of a homogeneous linear equation, ordinary and singular points for linear equations of the second order, solution near a singular point, method of Frobenius, singularities at infinity, simple examples of Boundary value problems for ordinary linear equation of the second order, Green’s functions, eigenvalues, eigenfunctions, Sturm-Liouville systems, properties of the gamma and beta functions, definition of the gamma function for negative values of the argument Legendre, Bessel, Chebyshev, Hypergeometic functions and orthogonality properties.

This course introduces students to the theory of boundary value and initial value problems for partial differential equations with emphasis on linear equations. Topics covered include first and second order partial differential equations, classification of second order linear partial differential equations, derivation of standard equation, methods of solution of initial and boundary value problems, separation of variables, Fourier series and their applications to boundary value problems in partial differential equation of engineering and physics, internal transform methods Fourier and Laplace transforms and their application to boundary value problems.

This course serves as an introduction to the field of operations research. It will quip students with scientific approaches to decision-making and mathematical modelling techniques required to design, improve and operate complex systems in the best possible way. Topics covered include linear programming, the simplex method, duality and sensitivity analysis, integer programming , nonlinear programming, dynamic programming and network models.

This is an introductory mechanics course designed to consolidate the understanding of fundamental concepts in mechanics such as force, energy, momentum etc. more rigorously as needed for further studies in physics, engineering and technology. Topcs covered include kinematics and dynamics of point masses, Newton’s laws, momentum, energy, angular momentum and torque, conservation laws, motion under gravity, central force problem, Virial theorem, Kepler’s laws, Rutherford problem, coupled oscillations, dynamics of rigid bodies, moment of inertia tensor, Euler’s equations, orthogonal transformation and Euler’s angle, Cayley Klein parameters, symmetric top, Lagrangian dynamics, generalized coordinates and forces, Lagrange’s equation, Hamilton’s principle, and variational methods.

This course introduces the principal algorithms for linear, network, discrete, nonlinear, dynamic optimization and optimal control. Emphasis is on methodology and the underlying mathematical structures. Topics include description of the problem of optimisation and the geometry of Rn, n > 1, convex sets and convex functions, unconstrained optimization: necessary and sufficient conditions for local minima/maxima, constrained optimization: equality and inequality constraints, Lagrange multipliers and the Kuhn-Tucker conditions, computational methods for unconstrained and constrained optimization, steepest descent and Newton's methods, quadratic programming, penalty and barrier methods, sequential quadratic programming (SQP) implementation in MATLAB/OCTAVE.

This course introduces the principal algorithms for linear, network, discrete, nonlinear, dynamic optimization and optimal control. Emphasis is on methodology and the underlying mathematical structures. Topics include description of the problem of optimisation and the geometry of Rn, n > 1, convex sets and convex functions, unconstrained optimization: necessary and sufficient conditions for local minima/maxima, constrained optimization: equality and inequality constraints, Lagrange multipliers and the Kuhn-Tucker conditions, computational methods for unconstrained and constrained optimization, steepest descent and Newton's methods, quadratic programming, penalty and barrier methods, sequential quadratic programming (SQP) implementation in MATLAB/OCTAVE.

**This course focuses on traditional algebra topics that have found greatest application in science and engineering as well as in mathematics. The topics covered include: Ideals and quotient rings, axioms for the integral domains, with examples, subdomains and subfields, ordered integral domains and fields, polynomial rings and field of quotients of an integral domain.**### Second Semester

This course is designed to offer a basic introduction to measure theory and Lebesgue’s integral. The topics to be covered are: countable and uncountable sets, countability of the rationals, uncountability of the reals, measurable sets and functions, the Lebesgue’s integral where E is a measurable subset of the real line and f is measurable on E, the spaces as metric spaces, Cauchy sequences in spaces, completeness of spaces, the Riesz-Fischer theorem and Mean convergence in the space .

This course provides an introduction to complex analysis which is the theory of complex functions of a complex variable. The topics to be covered in the course are: complex numbers, sequences and series of complex numbers, limits and continuity of functions of complex variables, elementary functions of a complex variable, Cauchy-Riemann criterion for differentiability, analytic functions, complex integrals, Taylor’s and Laurent’s series, calculus of residues, contour integration and conformal mapping.

This course is intended to introduce the student to the basic concepts and theorems of functional analysis and its applications. Topics covered include linear spaces, topological spaces, normed linear spaces & Banach Spaces, inner product spaces, Hilbert spaces, linear functional and the Hahn-Banach theorem.

This course develops concepts in quantum mechanics such that the behaviour of the physical universe can be understood from a fundamental point of view. It provides a basis for further study of quantum mechanics. Content will include: Historical origin of Quantum Theory: Blackbody radiation, Photoelectric effect, Compton effect, Optical Spectra of atoms. General formalism of Quantum theory: operators, wavefunctions and their physical significance, expectation value, commutation relations, uncertainty principle. The Schroedinger equation, infinite square well, the square well in three dimensions, central potential, step potential. The Harmonic Oscillator, Angular momentum in quantum mechanics. Approximation methods: Stationary Perturbation theory, Variational method, WKB approximation, Theory of Scattering.

This course is designed to equip students with the basic techniques for the efficient numerical solution of problems in science and engineering. Topics will include: Curve fitting and function approximation. Approximation formulae for kth derivatives. Composite rules and Romberg integration, Gauss quadrature, numerical method for multiple integrals. Numerical methods for ordinary differential equations. Numerical methods for Eigenvalues, the power method for finding dominant eigennvalues, the inverse power method for finding smallest eigenvalues, the shifted inverse power method, for finding an eigenvalues closest to a given approximate eigenvalue. Piece-wise polynomial interpolation, cubic splines.

This course introduces topology, covering topics fundamental to modern analysis and geometry. It also deals with subjects like topological spaces and continuous functions, connectedness, compactness, separation axioms, and further topics such as open and closed sets, neighbourhood, basis, convergence, limit point, completeness, subspaces, product spaces, quotient spaces.

## Programme Structure

### Level 100

### First Semester

Engaging in academic work at the university is challenging. This course is aimed at equipping fresh students to make the transition from pre-university level to the university level. It assists them in engaging and succeeding in complex academic tasks in speaking, listening, reading and writing. It also provides an introduction to university studies by equipping students with skills that will help them to engage in academic discourse with confidence and fluency.

This course seeks to prepare students for advanced courses in Mathematics. Students will have a better appreciation of how to perform basic operations on sets, real numbers and matrices and to prove and apply trigonometric identities. The specific topics that will be covered are: commutative, associative and distributive properties of union and intersection of sets. DeMorgan’s laws. Cartesian product of sets. The real number system natural numbers, integers, rational and irrational numbers. Properties of addition and multiplication on the set of real numbers. Relation of order in the system of real numbers. Linear, quadratic and other polynomial functions, rational algebraic functions, absolute value functions, functions containing radicals and their graphical representation. Inequalities in one and two variables. Application to linear programming. Indices and logarithms, their laws and applications. Binomial theorem for integral and rational indices and their application. Linear and exponential series. Circular functions of angles of any magnitude and their graphs. Trigonometric formula including multiple angles, half angles and identities. Solution to trigonometric equations.

### Second Semester

This is a follow-up course on the first semester one. It takes students through writing correct sentences, devoid of ambiguity, through the paragraph and its appropriate development to the fully-developed essay. The course also emphasizes the importance and the processes of editing written work.

### Level 200

### First Semester

This course aims to provide a first approach to the subject of algebra, which is one of the basic pillars of modern mathematics. The focus of the course will be the study of certain structures called groups, rings, fields and some related structures. Abstract algebra gives to student a good mathematical maturity and enable learners to build mathematical thinking and skill. The topics to be covered are injective, subjective and objective mappings. Product of mappings, inverse of a mapping. Binary operations on a set. Properties of binary operations (commutative, associative and distributive properties). Identity element of a set and inverse of an element with respect to a binary operation. Relations on a set. Equivalence relations, equivalence classes. Partition of set induced by an equivalence relation on the set. Partial and total order relations on a set. Well-ordered sets. Natural numbers mathematical induction. Sum of the powers of natural numbers and allied series. Integers divisors, primes, greatest common divisor, relatively prime integers, the division algorithm, congruencies, the algebra of residue classes. Rational and irrational numbers. Least upper bound and greatest lower bound of a bounded set of real numbers. Algebraic structures with one or two binary operations. Definition, examples and simple properties of groups, rings, integral domains and fields.

This course is designed to develop advanced topics of differential and integral calculus. Emphasis is placed on the applications of definite integrals, techniques of integration, indeterminate forms, improper integrals and functions of several variables. The topics to be covered are differentiation of inverse, circular, exponential, logarithmic, hyperbolic and inverse hyperbolic functions. Leibnitz’s theorem. Application of differentiation to stationary points, asymptotes, graph sketching, differentials, L’Hospital rule. Integration by substitution, by parts and by use of partial fractions. Reduction formulae. Applications of integration to plane areas, volumes and surfaces of revolution, arc length and moments of inertia. Functions of several variables, partial derivatives.

### Second Semester

The construction of mathematical models to address real-world problems has been one of the most important aspects of each of the branches of science. It is often the case that these mathematical models are formulated in terms of equations involving functions as well as their derivatives. Such equations are called differential equations. If only one independent variable is involved, often time, the equations are called ordinary differential equations. The course will demonstrate the usefulness of ordinary differential equations for modeling physical and other phenomena. Complementary mathematical approaches for their solution will be presented. The topics to be covered are vector algebra with applications to three-dimensional geometry. First order differential equations applications to integral curves and orthogonal trajectories. Ordinary linear differential equations with constant coefficients and equation reducible to this type. Simultaneous linear differential equations. Introduction to partial differential equations.

This course is designed to give an introduction to complex numbers and matrix algebra, which are very important in science and technology, as well as mathematics. The topics to be covered are complex numbers and algebra of complex numbers. Argand diagram, modulus-argument form of a complex number. Trigonometric and exponential forms of a complex number. De Moivre’s theorem, roots of unity, roots of a general complex number, nth roots of a complex number. Complex conjugate roots of a polynomial equation with real coefficients. Geometrical applications, loci in the complex plane. Transformation from the z-plane to the w-plane. Matrices and algebra of matrices and determinants, Operations on matrices up to . inverse of a matrix and its applications in solving systems of equation. Gauss-Jordan method of solving systems of equations. Determinants and their use in solving systems of linear equations. Linear transformations and matrix representation of linear transformations.

### Level 300

### First Semester

This course covers the fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, and the interchange of limit operations. It shows the utility of abstract concepts and teaches an understanding and construction of proofs. The topics to be covered include

limit of a sequence of real numbers, standard theorems on limits, bounded and monotonic sequences of real numbers, infinite series of real numbers, tests for convergence, power series, limit, continuity and differentiability of functions of one variable, Rolle’s theorem, mean value theorems, Taylor’s theorem, definition and simple properties of the Riemann integral.

This course introduces more algebraic methods needed to understand real world questions. It develops fundamental algebraic tools involving matrices and vectors to study linear systems of equations and Gaussian elimination, linear transformations, orthogonal projection, least squares, determinants, eigenvalues and eigenvectors and their applications. The topics to be covered are axioms for vector spaces over the field of real and complex numbers. Subspaces, linear independence, bases and dimension. Row space, Column space, Null space, Rank and Nullity. Inner Products Spaces. Inner products, Angle and Orthogonality in Inner Product Spaces, Orthogonal Bases, Gram-Schmidt orthogonalization process. Best Approximation. Eigenvalues and Eigenvectors. Diagonalization. Linear transformation, Kernel and range of a linear transformation. Matrices of Linear Transformations.

Limit and continuity of functions of several variables partial derivatives, differentials, composite, homogenous and implicit functions Jacobians, orthogonal curvilinear coordinates multiple integral, transformation of multiple integrals Mean value and Taylor’s Theorems for several variables maxima and minima with applications.

### Second Semester

**This course covers vector valued functions. It introduces students to the concept of change and motion and the manner in which quantities approach other quantities. Topics include limits, continuity, derivatives of vector functions, gradient, divergence, curl, formulae involving gradient, divergence, laplacian, orthogonal curvilinear coordinates, line integrals, Green’s theorem in the plane, surface integrals. Other topics are the divergence theorem, improper integrals, Gamma functions, Beta functions, the Riemann Stieltjes Integral, pointwise and uniform convergence of sequence and series, integration and differentiation term by term.**Limits, continuity and derivatives of vector functions gradient, divergence and curl formulae involving gradient, divergence, curl and laplacian and orthogonal curvilinear coordinates line integrals Green’s theorem in the plane surface integrals the divergence theorem improper integrals Gamma and Beta functions The Riemann Stieltjes integral pointwise and uniform convergence of sequence and series integration and differentiation term by term.

This course introduces more algebraic methods needed to understand real world questions. It develops fundamental algebraic tools involving direct sum of subspaces, complement of subspace in a vector space and dimension of the sum of two subspaces. Other topics to be covered are one-to one, onto and bijective linear transformations, isomorphism of vector spaces, matrix of a linear transformation relative to a basis, orthogonal transformations, rotations and reflections, real quadratic forms, and positive definite forms.

This course focuses on traditional algebra topics that have found greatest application in science and engineering as well as in mathematics. The topics to be covered are: axioms for groups with examples, subgroups, simple properties of groups, cyclic groups, homomorphism and isomorphism, axioms for rings, and fields, with examples, simple properties of rings, cosets and index of a subgroup, Lagrange’s theorem, normal subgroups and quotient groups, the residual class ring, homomorphism and isomorphism of rings, subrings.

### Level 400

### First Semester

The construction of mathematical models to address real-world problems has been one of the most important aspects of each of the branches of science. It is often the case that these mathematical models are formulated in terms of equations involving functions as well as their derivatives. Such equations are called differential equations. If only one independent variable is involved, often time, the equations are called ordinary differential equations. The course will demonstrate the usefulness of ordinary differential equations for modelling physical and other phenomena. Complementary mathematical approaches for their solution will be presented. Topics covered include linear differential equation of order n with coefficients continuous on some interval J, existence-uniqueness theorem for linear equations of order n, determination of a particular solution of non-homogeneous equations by the method of variation of parameters, Wronskian matrix of n independent solutions of a homogeneous linear equation, ordinary and singular points for linear equations of the second order, solution near a singular point, method of Frobenius, singularities at infinity, simple examples of Boundary value problems for ordinary linear equation of the second order, Green’s functions, eigenvalues, eigenfunctions, Sturm-Liouville systems, properties of the gamma and beta functions, definition of the gamma function for negative values of the argument Legendre, Bessel, Chebyshev, Hypergeometic functions and orthogonality properties.

This course introduces students to the theory of boundary value and initial value problems for partial differential equations with emphasis on linear equations. Topics covered include first and second order partial differential equations, classification of second order linear partial differential equations, derivation of standard equation, methods of solution of initial and boundary value problems, separation of variables, Fourier series and their applications to boundary value problems in partial differential equation of engineering and physics, internal transform methods Fourier and Laplace transforms and their application to boundary value problems.

## Course Descriptions

This course provides opportunities for students to strengthen their mathematical skills and understanding of rational numbers using contextual, real-life problems. This course is graded on a pass/fail basis. To pass the course, a student must earn a 77% or better.

### MAT 110Math Essentials3 credits

This course provides a basic introduction to linear functions. Topics include: identify, simplify, and evaluate polynomials solve linear equations and inequalities, including systems graph linear equations and inequalities. Credit for this course applies toward graduation as an elective. Please note that the minimum passing grade is a ''C.''

*Prerequisite(s): Pass math skills assessment or MAT 095.*### MAT 200Pre-Calculus3 credits

This course provides an integrated review of intermediate algebra, analytic geometry, and basic trigonometry in order to prepare the student for calculus. After a brief review of linear and quadratic functions, the course covers graphs and applications for polynomial, rational, exponential, logarithmic, and trigonometric functions. The course also incorporates matrices and vectors. Please note that a minimum grade of C is required in order for students to take Calculus I (MAT 310).

*Prerequisite(s): MAT 121 or MAT 205 with a minimum grade of ''C'' or college algebra equivalent.*### MAT 201Mathematics for Teachers I3 credits

This class will prepare teacher candidates to become effective mathematics teachers in their own classrooms. Through mathematical investigations, candidates will learn the underlying concepts, structures, functions and patterns that promote mathematical reasoning and understanding. Candidates will investigate how moving progressively through essential topics deepens their understanding of mathematics. Students will use the National Council of Teachers of Mathematics Standards and STEM strategies. Various methods such as modeling, collaboration, manipulatives, thinking made visible, and writing across the curriculum will be presented for bridging classroom activities and real-world problem solving. Teacher candidates will learn how to analyze their students&rsquo math-solving processes by developing thorough explanations of their own mathematical understanding and critiquing the explanation of others&rsquo mathematical understandings. Candidates will communicate their mathematical ideas, processes, analyses and understandings through both writing and speaking. This course concentrates on

*numbers and operations*and their application to student learning and classroom teaching.*Prerequisite(s): Successfully passing math skills assessment or MAT 110 with a minimum grade of C.*### MAT 202Mathematics for Teachers II3 credits

This class will prepare teacher candidates to become effective mathematics teachers in their own classrooms. Through mathematical investigations candidates will learn the underlying concepts, structures, functions and patterns that promote mathematical reasoning and understanding. Candidates will investigate how moving progressively through essential topics deepens their understanding of mathematics. Students will use the National Council of Teachers of Mathematics Standards and STEM strategies. Various methods such as modeling, collaboration, manipulatives, thinking made visible, and writing across the curriculum will be presented for bridging classroom activities and real-world problem solving. Teacher candidates will learn how to analyze their students&rsquo math-solving processes by developing thorough explanations of their own mathematical understanding and critiquing the explanation of others&rsquo mathematical understandings. Candidates will communicate their mathematical ideas, processes, analyses and understandings through both writing and speaking. This course concentrates on

*geometry, measurement, probability and statistics*and their application to student learning and classroom teaching.*Prerequisite(s): MAT 201 with a minimum grade of C.*### MAT 205Introductory Survey of Mathematics3 credits

This course introduces a broad range of topics in mathematics, including algebra, probability, and statistics. After reviewing linear functions, algebraic topics include solving and graphing quadratic and exponential functions. Topics in probability include counting principles, combinations, permutations, compound events, mutually exclusive events, and independent events. Topics in statistics include measures of central tendency, measures of dispersion, and the normal curve. Please note that the minimum passing grade for this course is a ''C.''

*Prerequisite(s): Pass math skills assessment or MAT 110 with a minimum grade of ''C''.*### MAT 304Mathematics for Teachers III3 credits

This class will prepare teacher candidates to become effective mathematics teachers in their own classrooms. Through mathematical investigations candidates will learn the underlying concepts, structures, functions and patterns that promote mathematical reasoning and understanding. Candidates will investigate how moving progressively through essential topics deepens their understanding of mathematics. Students will use Common Core Mathematics Standards and STEM strategies. Various methods such as modeling, collaboration, manipulatives, thinking made visible, and writing across the curriculum will be presented for bridging classroom activities and real-world problem solving. Teacher candidates will learn how to analyze their students&rsquo math-solving processes by developing thorough explanations of their own mathematical understanding and critiquing the explanation of others&rsquo mathematical understandings. Candidates will communicate their mathematical ideas, processes, analyses and understandings through both writing and speaking. This course concentrates on

*algebra and functions*and their application to student learning and classroom teaching.*Prerequisite(s): MAT 202 with a minimum grade of C.*### MAT 308Inferential Statistics3 credits

This course introduces the student to the scientific method of collecting, organizing, and interpreting data in real-world applications, such as behavioral science, communication, education, healthcare, manufacturing, and natural science. Students will use graphing calculators, along with Excel, to assist in displaying and analyzing data.

*Prerequisite(s): MAT 122 or MAT 202 or MAT 205 with minimum grade of ''C'' or BSN candidate.*### MAT 310Calculus I3 credits

After a brief review of classes of functions and their properties, this course focuses on students' understanding and application of limits, continuity, techniques for finding the derivative, use of the derivative in graphing functions, applications of the derivative, implicit differentiation, anti-derivatives, areas under the curve, the Fundamental Theorem of Calculus, integration by substitution and differential equations. Students are required to explain their reasoning graphically, numerically, analytically, and verbally.

*Prerequisite(s): MAT 200 with a minimum grade of ''C''.*### MAT 311Calculus II3 credits

After a review of limits and derivatives, this course focuses on students' understanding and application of antiderivatives, the definite integral, the Fundamental Theorem of Calculus, integration techniques, applications of the definite integral and improper integrals. An overview of multivariable calculus includes partial derivatives, minima and maxima, and double integrals. The course concludes with a discussion of Taylor series and L'Hospital's rule. Students are required to explain their reasoning graphically, numerically, analytically, and verbally.

### MAT 312Business Statistics3 credits

This course introduces the student to the scientific method of collecting, organizing, and interpreting data in a variety of business applications. Students will use Excel to assist in displaying and analyzing data.

*Prerequisite(s): MAT 205 or MAT 122 with a minimum grade of ''C'' or College of Business completion degree candidate.*### MAT 313Experimental Design3 credits

*Prerequisite(s): MAT 308 or MAT 312 with a minimum grade of C.*### MAT 314Regression Analysis for the Social Sciences3 credits

*Prerequisite(s): MAT 308 or MAT 312 with a minimum grade of C.*### MAT 320Finite Mathematics3 credits

This course provides a survey of selected topics in mathematics, with emphasis on problem solving and applications. Algebra and functions will be reviewed. Core topics include exponential and logarithmic functions, interest, annuities, systems of linear equations, matrix operations, linear programming, the simplex method, set theory, probability, and counting theory.

*Prerequisite(s): MAT 304, MAT 205, MAT 121 or college algebra equivalent.*### MAT 330Discrete Math3 credits

This course provides an introduction to discrete mathematics. Topics include sets, functions and relations, mathematical induction and logic, sequences and recursion, and an introduction to Boolean algebra.

*Prerequisite(s): MAT 200 and MAT 320*### MAT 331Geometry3 credits

This course presents the core concepts and principles of Euclidean geometry in two and three dimensions. Topics include geometric constructions, congruence, similarity, transformations, measurement, and coordinate geometry. Axiomatic systems and proofs are covered. An overview of non-Euclidean geometries is provided.

### MAT 332History of Mathematics3 credits

This course provides an overview of the historical evolution of major concepts in mathematics including counting and number systems, geometry, algebra, calculus, and statistics. The contributions of various civilizations ranging from Babylonia and Egypt through Greece and the Middle East to the modern world are reviewed. Biographical sketches of some of the individuals who made major contributions to the development of mathematics are presented. The interrelationship between the evolution of mathematics, science, and technology is explored.

## MAT: Mathematics

Development of quantitative thinking and problem solving abilities through a selection of mathematical topics: logic and reasoning numbers, functions, and modeling combinatorics and probability growth and change. Other topics may include geometry, statistics, game theory, and graph theory. Through their engagement in problem solving, students develop an appreciation of the intellectual scope of mathematics and its connections with other disciplines.

Prerequisite: C or better in MAP 103 or level 2+ or higher on the mathematics placement examination

(Prerequisite must be met within one year of beginning this course.)

### MAT 119: Foundations for Precalculus

This course is a companion to MAT 123: Precalculus, providing a structured environment where students can refresh the algebra skills which are necessary for success in precalculus. These topics include understanding of exponents (especially fractional and negative exponents), manipulating mathemematical expressions, solving equations, and modeling/word problems. Course may not be taken with CHE 129.

Prerequisite: 2+ on placement or permission of MAT 123 instructor

### MAT 122: Overview of Calculus with Applications

The basics of calculus in a self-contained, one-semester course. Properties and applications of polynomial, exponential, and logarithmic functions. Derivatives: slopes, rates of change, optimization, integrals, area, cumulative change, and average. The fundamental theorem of calculus. Emphasis on modeling examples from economics. Students who subsequently wish to enroll in MAT 125 or 131 will be required to score level 4 on the mathematics placement examination before taking either course. This course has been designated as a High Demand/Controlled Access (HD/CA) course. Students registering for HD/CA courses for the first time will have priority to do so.

Prerequisite: C or better in MAP 103 or level 3 on the mathematics placement exam

(Prerequisite must be met within one year prior to beginning the course.)

### MAT 123: Precalculus

Comprehensive preparation for the regular calculus sequences. Careful development of rational, exponential, logarithmic, and trigonometric functions, and their applications. Asymptotics and curve sketching. General modeling examples. This course has been designated as a High Demand/Controlled Access (HD/CA) course. Students registering for HD/CA courses for the first time will have priority to do so.

Prerequisite: C or better in MAP 103 or level 3 on the mathematics placement exam or corequisite MAT 119 (Prerequisite must be met within one year prior to beginning the course.)

### MAT 125: Calculus A

Differential calculus, emphasizing conceptual understanding, computations and applications, for students who have the necessary background from 12th-year high school mathematics. Limits and continuous functions. Differentiation of elementary algebraic, trigonometric, exponential and logarithmic functions graphing modeling and maximization. L'Hospital's rule. May not be taken for credit in addition to MAT 131 or 141 or AMS 151. This course has been designated as a High Demand/Controlled Access (HD/CA) course. Students registering for HD/CA courses for the first time will have priority to do so.

Prerequisite: C or higher in MAT 123 or level 4 on the mathematics placement examination or corequisite MAT 130

### MAT 126: Calculus B

A continuation of MAT 125, covering integral calculus: Riemann sums, the fundamental theorem, symbolic and numeric methods of integration, area under a curve, volume, applications such as work and probability, improper integrals. This course has been designated as a High Demand/Controlled Access (HD/CA) course. Students registering for HD/CA courses for the first time will have priority to do so.

Prerequisite: C or higher in MAT 125 or 131 or 141 or AMS 151 or level 6 on the mathematics placement examination

### MAT 127: Calculus C

A continuation of MAT 126, covering: sequences, series, Taylor series, differential equations and modeling. May not be taken for credit in addition to MAT 132, MAT 142, MAT 171, or AMS 161. This course has been designated as a High Demand/Controlled Access (HD/CA) course. Students registering for HD/CA courses for the first time will have priority to do so.

Prerequisite: C or higher in MAT 126 or level 8 on the mathematics placement examination

### MAT 130: Trigonometry and Logarithms

Inverse functions, exponential and logarithmic functions, radian measure of angles and trigonometric functions. Taught as a companion to MAT 125.

Prerequisite: MAT 122 with a grade of C or better, or level 3+ or higher on the placement exam, or permission of instructor

### MAT 131: Calculus I

The differential calculus and integral calculus, emphasizing conceptual understanding, computations and applications, for students who have the necessary background from 12th-year high school mathematics. Differentiation of elementary algebraic trigonometric, exponential, and logarithmic functions graphing modelling and maximization L'Hospital's rule the Riemann integral and the Fundamental Theorem of Calculus. May not be taken for credit in addition to MAT 125 or 141 or AMS 151. This course has been designated as a High Demand/Controlled Access (HD/CA) course. Students registering for HD/CA courses for the first time will have priority to do so.

Prerequisite: B or higher in MAT 123 or level 5 on the mathematics placement examination

### MAT 132: Calculus II

A continuation of MAT 131, covering symbolic and numeric methods of integration area under a curve volume applications such as work and probability sequences series Taylor series differential equations and modelling. May not be taken for credit in addition to MAT 127, MAT 142, MAT 171, or AMS 161. This course has been designated as a High Demand/Controlled Access (HD/CA) course. Students registering for HD/CA courses for the first time will have priority to do so.

Prerequisite: C or higher in AMS 151 or MAT 131 or 141, or level 7 on the mathematics placement examination

### MAT 141: Analysis I

A careful study of the theory underlying calculus. The development of the real number system, limits and infinite sequences, functions of one real variable, continuity, differentiability, the Riemann integral, and the Fundamental Theorem of Calculus. Full attention to proofs is given. All topics in MAT131 are included, although the presentation differs significantly. May not be taken for credit in addition to MAT 125, MAT 131, or AMS 151. A student who successfully completes both MAT 141 and 142 will receive equivalency for MAT 320. This course has been designated as a High Demand/Controlled Access (HD/CA) course. Students registering for HD/CA courses for the first time will have priority to do so.

Prerequisite: Level 5 on the mathematics placement examination priority given to students in the University's honors programs

### MAT 142: Analysis II

A continuation of MAT 141 in the same spirit, including the topics of MAT 132 but with attention to theory and including proofs of major theorems: techniques and applications of integration, infinite series, Taylor series, modelling and elementary differential equations. A student who successfully completes both MAT 141 and MAT 142 will receive a waiver for MAT 320. May not be taken for credit in addition to MAT 127, MAT 171, or AMS 161. This course has been designated as a High Demand/Controlled Access (HD/CA) course. Students registering for HD/CA courses for the first time will have priority to do so.

Prerequisite: C or higher in MAT 141 or permission of the Advanced Track Committee

### MAT 171: Accelerated Single-Variable Calculus

A single semester, honors-level, course which reviews the material in MAT 131 in a few weeks, then concentrates on the topics covered in MAT 132, with additional attention paid to the underlying theory. Primarily intended for students who have had calculus in high school. May not be taken for credit in addition to MAT 126, MAT 127, MAT 132, MAT 142, or AMS 161.

Prerequisites: Level 5 on the AB Calculus AP exam, Level 3 on the BC Calculus exam, A or A- in MAT 131 or AMS 151, MAT 141, or level 7 on the mathematics placement exam. Priority given to students in the University's honors programs.

### MAT 200: Logic, Language and Proof

A basic course in the logic of mathematics, the construction of proofs and the writing of proofs. The mathematical content is primarily logic and proofs, set theory, combinatorics, functions and relations. There is considerable focus on writing. May not be taken for credit in addition to MAT 250.

Prerequisite: Level 4 on the mathematics placement examination or equivalent course or permission of the instructor

### MAT 203: Calculus III with Applications

Vector algebra in two and three dimensions, multivariate differential and integral calculus, optimization, vector calculus including the theorems of Green, Gauss, and Stokes. Applications to economics, engineering, and all sciences, with emphasis on numerical and graphical solutions use of graphing calculators or computers. May not be taken for credit in addition to AMS 261.

Prerequisite: C or higher in MAT 127 or 132 or 142 or AMS 161 or level 9 on the mathematics placement examination

### MAT 211: Introduction to Linear Algebra

Introduction to the theory of linear algebra with some applications vectors, vector spaces, bases and dimension, applications to geometry, linear transformations and rank, eigenvalues and eigenvectors, determinants and inner products. May not be taken for credit in addition to AMS 210.

Prerequisite: C or higher in AMS 151 or MAT 131 or 141 or coregistration in MAT 126 or level 7 on the mathematics placement examination

### MAT 220: Linear Algebra and Geometry

Vectors and vector algebra. Dot product. Cross product and triple product. Analytic geometry. Vector equations of lines and planes. Curves and surfaces of degree two. Complex numbers. Linear spaces and linear maps. Matrices, systems of linear equations. Isomorphisms of vector spaces, bases and dimension. MAT 220 is primarily intended for students in the Advanced Track program. It serves as an alternative to MAT 211 and may not be taken for credit in addition to MAT 211.

Prerequisite: MAT 131 or an equivalent course or level 7 or higher on mathematics placement examination or permission of the Advanced Track Committee

### MAT 250: Introduction to Advanced Mathematics

An introduction to the Advanced Track mathematics program. Provides the core of basic of propositional logic, quantifiers, proofs, sets, functions, cardinality, relations, equivalence relations and quotient sets, order relations, combinatorics. Number systems: natural numbers, integers, rational, real and complex numbers. MAT 250 is primarily intended for students in the Advanced Track program. It serves as an alternative to MAT 200 and may not be taken for credit in addition to MAT 200. Formerly offered as MAT 150 not for credit in addition to MAT 150.

Prerequisite: MAT 131 or an equivalent course or level 7 or higher on mathematics placement examination or permission of the Advanced Track Committee.

### MAT 260: Problem Solving in Mathematics

Students actively solve challenging problems in plane geometry, basic number theory, and calculus, and write precise arguments. Relevant preparation for problem-solving is provided in the course.

Prerequisite: Permission of instructor

### MAT 303: Calculus IV with Applications

Homogeneous and inhomogeneous linear differential equations systems of linear differential equations series solutions Laplace transforms Fourier series. Applications to economics, engineering, and all sciences with emphasis on numerical and graphical solutions use of computers. May not be taken for credit in addition to AMS 361 or MAT 308.

Prerequisite: C or higher in MAT 127 or 132 or 142 or AMS 161 or level 9 on the mathematics placement examination

### MAT 307: Multivariable Calculus with Linear Algebra

Introduction to linear algebra: vectors, matrices, systems of linear equations, bases and dimension, dot product, determinants. Multivariate differential and integral calculus, divergence and curl, line and surface integrals, theorems of Green, Gauss, and Stokes. More theoretical and intensive than MAT 203, this course is primarily intended for math majors. Together with MAT 308, it forms a 2-semester sequence covering the same material as the 3-semester sequence of MAT 203, MAT 211 and MAT 303. May not be taken for credit in addition to MAT 203 or AMS 261.

Prerequisite: MAT 127 or MAT 132

### MAT 308: Differential Equations with Linear Algebra

Linear algebra: determinants, eigenvalues and eigenvectors, diagonalization. Differential equations existence and uniqueness of solutions. First- and second-order equations linear versus nonlinear equations. Systems of linear equations. Laplace transform. Applications to physics. More theoretical and intensive than MAT 303, this course is primarily intended for math majors. Together with MAT 307, it forms a 2-semester sequence covering the same material as the 3-semester sequence of MAT 205, MAT 211 and MAT 305. May not be taken for credit in addition to MAT 303 or AMS 361.

Prerequisite: MAT 307 or MAT 203 and MAT 211 or MAT 132 and MAT 220 or permission of instructor

### MAT 310: Linear Algebra

Finite dimensional vector spaces, linear maps, dual spaces, bilinear functions, inner products. Additional topics such as canonical forms, multilinear algebra, numerical linear algebra.

Prerequisite: C or higher in MAT 211 or 308 or AMS 210 or MAT 220 C or higher in MAT 200 or MAT 250 or permission of instructor

### MAT 311: Number Theory

Congruences, quadratic residues, quadratic forms, continued fractions, Diophantine equations, number-theoretical functions, and properties of prime numbers.

Prerequisites: C or higher in MAT 312 or 313 C or higher in MAT 200 or MAT 250 or permission of instructor

### MAT 312: Applied Algebra

Topics in algebra: groups, informal set theory, relations, homomorphisms. Applications: error correcting codes, Burnside's theorem, computational complexity, Chinese remainder theorem. This course is offered as both AMS 351 and MAT 312.

Prerequisite: C or higher in AMS 210 or MAT 211 or MAT 220

Advisory Prerequiste: MAT 200 or CSE 215 or CSE 150 or equivalent

### MAT 313: Abstract Algebra

Groups and rings together with their homomorphisms and quotient structures. Unique factorization, polynomials, and fields.

Prerequisite: C or higher in MAT 310 or MAT 312 or MAT 315 C or higher in MAT 200 or MAT 250 or permission of instructor

### MAT 314: Abstract Algebra II

This course is a continuation of MAT 313, Abstract algebra. It covers modules over rings, including structure theorem for modules over PID, theory of fields and field extensions and introduction to Galois theory.

Prerequisite: MAT 313 or permission of the instructor

### MAT 315: Advanced Linear Algebra

Finite dimensional vector spaces over a field, linear maps, isomorphisms, dual spaces, quotient vector spaces, bilinear and quadratic functions, inner products, canonical forms of linear operators, multilinear algebra, tensors. This course serves as an alternative to MAT 310. It is an intensive course, primarily intended for math majors in Advanced Track program.

Prerequisite: B or higher in MAT 200 or MAT 250, and B or higher in MAT 220, or permission of the instructor

### MAT 319: Foundations of Analysis

A careful study of the theory underlying topics in one-variable calculus, with an emphasis on those topics arising in high school calculus. The real number system. Limits of functions and sequences. Differentiations, integration, and the fundamental theorem. Infinite series.

Prerequisite: C or higher in MAT 200 or MAT 250 or permission of instructor C or higher in one of the following: MAT 203, 211, 220, 307, AMS 261, or A- or higher in MAT 127, 132, 142, or AMS 161

### MAT 320: Introduction to Analysis

A careful study of the theory underlying calculus. The real number system. Basic properties of functions of one real variable. Differentiation, integration, and the inverse theorem. Infinite sequences of functions and uniform convergence. Infinite series. Metric spaces and compactness. This course is a more demanding alternative of MAT 319, suitable for students who are comfortable with rigorous proofs.

Prerequisite: B or higher in MAT 200 or MAT 250 or permission of instructor C or higher in one of the following: MAT 203, 211, 220, 307, AMS 261, or A- or higher in MAT 127, 132, 142, or AMS 161

### MAT 322: Analysis in Several Dimensions

Continuity, differentiation, and integration in Euclidean n-space. Differentiable maps. Implicit and inverse function theorems. Differential forms and the general Stokes's theorem.

Prerequisites: C or higher in MAT 203, MAT 220, MAT 307, or AMS 261 C or higher in MAT 310 or MAT 315 B or higher in MAT 320

### MAT 324: Real Analysis

Introduction to Lebesgue measure and integration. Aspects of Fourier series, function spaces, Hilbert spaces, Banach spaces.

Prerequisites: B or higher in MAT 320

### MAT 331: Computer-Assisted Mathematical Problem Solving

Exploration of the use of the computer as a tool to gain insight into complex mathematical problems through a project-oriented approach. Students learn both the relevant mathematical concepts and ways that the computer can be used (and sometimes misused) to understand them. The particular problems may vary by semester past topics have included cryptography, fractals and recursion, modeling the flight of a glider, curve fitting, the Brachistochrone, and computer graphics. No previous experience with computers is required.

Prerequisite: C or higher in MAT 203 or 205 or 307 or AMS 261

### MAT 336: History of Mathematics

A survey of the history of mathematics from the beginnings through the 19th century, with special attention to primary sources and to the interactions between culture and mathematics. Emphasis on topics germane to the high school curriculum. Mesopotamian, Egyptian, and Greek mathematics non-European mathematics early Renaissance mathematics the birth and flowering of calculus the beginnings of probability theory and the origin of non-Euclidean geometries and the modern concept of number.

Prerequisite: MAT 200 or MAT 203 or or MAT 250 or MAT 307 or AMS 261

### MAT 341: Applied Real Analysis

Partial differential equations of mathematical physics: the heat, wave, and Laplace equations. Solutions by techniques such as separation of variables using orthogonal functions (e.g., Fourier series, Bessel functions, Legendre polynomials). D'Alambert solution of the wave equation.

Prerequisites: C or higher in the following: MAT 203 or 220 or 307 or AMS 261 MAT 303 or 305 or 308 or AMS 361

Advisory Prerequisite: MAT 200 or MAT 250

### MAT 342: Applied Complex Analysis

Complex numbers, analytic functions, the Cauchy-Riemann and Laplace equations, the Cauchy integral formula and applications. Fundamental Theorem of Algebra and the Maximum Principle. The Cauchy residue theorem and applications to evaluating real integrals. Conformal mappings.

Prerequisite: C or higher in the following: MAT 203 or MAT 220 or MAT 307 or AMS 261

Advisory Prerequisite: MAT 200 or MAT 250

### MAT 351: Differential Equations: Dynamics and Chaos

A study of the long-term behavior of solutions to ordinary differential equations or of iterated mappings, emphasizing the distinction between stability on the one hand and sensitive dependence and chaotic behavior on the other. The course describes examples of chaotic behavior and of fractal attractors, and develops some mathematical tools for understanding them.

Prerequisites: C or higher in the following: MAT 203 or MAT 220 or MAT 307 or AMS 261 MAT 303 or MAT 308 or AMS 361 MAT 200 or MAT 250 or permission of instructor

### MAT 360: Geometric Structures

Formal geometries and models. Topics selected from projective, affine, Euclidean, and non-Euclidean geometries.

Pre- or Corequisites: MAT 203 or 220 or 307 or AMS 261 MAT 200 or MAT 250 or permission of instructor

### MAT 362: Differential Geometry of Surfaces

The local and global geometry of surfaces: geodesics, parallel transport, curvature, isometries, the Gauss map, the Gauss-Bonnet theorem.

Prerequisite: C or higher in MAT 319 or MAT 320 or MAT 364 MAT 203 or MAT 307 or MAT 322

### MAT 364: Topology and Geometry

A broadly based introduction to topology and geometry, the mathematical theories of shape, form, and rigid structure. Topics include intuitive knot theory, lattices and tilings, non-Euclidean geometry, smooth curves and surfaces in Euclidean 3-space, open sets and continuity, combinatorial and algebraic invariants of spaces, higher dimensional spaces.

Prerequisites: MAT 203 or 220 or 307 or AMS 261 MAT 200 or 250

Advisory Prerequisite: MAT 319 or 320

### MAT 371: Logic

A survey of the logical foundations of mathematics: development of propositional calculus and quantification theory, the notions of a proof and of a model, the completeness theorem, Goedel's incompleteness theorem. This course is offered as both CSE 371 and MAT 371.

Prerequisite: CSE 150 or CSE 215 or MAT 200 or MAT 250

### MAT 373: Analysis of Algorithms

Mathematical analysis of a variety of computer algorithms including searching, sorting, matrix multiplication, fast Fourier transform, and graph algorithms. Time and space complexity. Upper-bound, lower- bound, and average-case analysis. Introduction to NP completeness. Some machine computation is required for the implementation and comparison of algorithms. This course is offered as CSE 373 and MAT 373. Not for credit in addition to CSE 385.

Prerequisites: C or higher in MAT 211 or AMS 210 CSE 214 or CSE 260

### MAT 401: Seminar in Mathematics

Discussions of a specific area of interest in mathematics. The work of each semester covers a different area of mathematics. May be repeated as topic changes. Prerequisites will be announced with the topic each time the course is offered.

Prerequisite: U3/U4 permission of department or instructor additional prerequisites announced with topic

### MAT 402: Seminar in Mathematics

Discussions of a specific area of interest in mathematics. The work of each semester covers a different area of mathematics. May be repeated as topic changes. Prerequisites will be announced with the topic each time the course is offered.

Prerequisite: U3/U4 permission of department or instructor additional prerequisites announced with topic

### MAT 425: How to teach remedial mathematics

Provides knowledge and skills for teaching college remedial mathematics classes. It includes analysis of difficulties that students encounter in the mathematical college courses of initial levels. In it, precollege mathematics is revisited, its usage in college courses is discussed, and, on the basis of this concrete material, students are taught how to detect and treat typical mistakes and misconceptions, how to compose problems and tests, how to analyze and assess pro-actively students¿ works, and how to organize lessons in the environment of students with diverse challenges and needs. Students will learn how to present mathematics clearly and mathematically correct both verbally and in writing.

Prerequisite: MAT 200 and grade B or higher in one of the Calculus classes

### MAT 444: Experiential Learning

This course is designed for students who engage in a substantial, structured experiential learning activity in conjunction with another class. Experiential learning occurs when knowledge acquired through formal learning and past experience are applied to a "real-world" setting or problem to create new knowledge through a process of reflection, critical analysis, feedback and synthesis. Beyond-the-classroom experiences that support experiential learning may include: service learning, mentored research, field work, or an internship.

Prerequisite: WRT 102 or equivalent permission of the instructor and approval of the EXP+ contract (http://sb.cc.stonybrook.edu/bulletin/current/policiesandregulations/degree_requirements/EXPplus.php)

### MAT 458: Speak Effectively Before an Audience

A zero credit course that may be taken in conjunction with any MAT course that provides opportunity to achieve the learning outcomes of the Stony Brook Curriculum's SPK learning objective.

Pre- or corequisite: WRT 102 or equivalent permission of the instructor

### MAT 459: Write Effectively in Mathematics

A zero credit course that may be taken in conjunction with any 300- or 400-level MAT course, with permission of the instructor. The course provides opportunity to practice the skills and techniques of effective academic writing and satisfies the learning outcomes of the Stony Brook Curriculum's WRTD learning objective.

Prerequisite: WRT 102 permission of the instructor

### MAT 475: Undergraduate Teaching Practicum

Each student assists in teaching a lower-division mathematics course or works in the Mathematics Learning Center. The student's work is regularly supervised by a faculty member. In addition, a weekly seminar is conducted. Responsibilities may include preparation of materials for student use and discussions, helping students with problems, and involvement in "alternative" teaching projects. Intended for upper-division students who have excelled in the calculus sequence. May not be used for major credit.

Prerequisite: Permission of the director of undergraduate studies

### MAT 487: Independent Study in Special Topics

A reading course for juniors and seniors. The topics may be chosen by the student with the approval of a supervising member of the faculty, who also takes responsibility for evaluation. A topic that is covered in a course regularly offered by the department is not appropriate for independent study. May be repeated.

Prerequisite: Permission of the director of undergraduate studies

### MAT 495: Honors Thesis

The student and a supervising faculty member together choose a topic in mathematics, and the student writes a substantial paper expounding the topic in a new way.

## Math 2413: Calculus I

Please make sure you have the necessary prerequisites for this course: Satisfactory scores on both the ACC Mathematics Assessment and Higher Level Placement Tests OR departmental approval.

You should bring your homework to class every day. It will be collected regularly. There will also be in-class assignments or quizzes collected for a grade (as part of your homework grade). There will be a penalty on late homework. Homework that is more than a week late might not receive any credit. If you do not follow the instructions that will be announced in class about how to organize and submit your homework, you may not receive full (or any) credit for it.

**Text**:*Calculus: Concepts and Contexts,*4th ed., by James Stewart, Brooks/Cole 2010**Please Note:**For Calculus I and Calculus II, the Single Version (SV) is required. ISBN 9781111027308 For Calculus III, the Multivariable Version (MV) is required. ISBN 9780538460293 You can purchase a Full Version of the text that includes all material for Calculus I, II, and III if you plan to take the entire sequence at Austin Community College. ISBN 9780538796859**Online Componen**t: Enhanced WebAssign (EWA) may be required for one or all of the Calculus courses. (It will not be required for this class.) Access to EWA includes a complete online eBook. You may purchase EWA access in one of three ways:· Bundled textbooks with access codes are available at ACC bookstores.

· Bundled textbooks with access codes are available for purchase and delivery from the publisher. http://www.cengagebrain.com/course/site.html?id=1-1UATASJ

· You may use a credit card or PayPal to purchase EWA access online with the online book if you do not want a hardcover book from the website above.

It is recommended that you register for EWA when you purchase your textbook regardless of whether or not your initial instructor requires the program. Please refer to the handout for login and enrollment information.

*Student Solutions Manual*, ISBN 9780495560616 , by Jeffrey A. Cole**REQUIRED TECHNOLOGY**:

You must have access to technology that enables you to (1) Graph a function, (2) Find the zeroes of a function. Most ACC faculty are familiar with the TI family of graphing calculators. Hence, TI calculators are highly recommended for student use. Other calculator brands can also be used. Your instructor will determine the extent of calculator use in your class section.There will be 3 exams plus a final exam (part of which will be comprehensive). Grades will be weighted as follows:

Sometime after Test 3, there will be a single make-up exam over the material on tests 1-3 the grade on this exam can be used to replace your lowest grade on the first three tests, up to a maximum grade of 85 if you make complete corrections for tests 1-3 or 70 without the completed corrections.

If you take any test late for any reason, there will be a penalty of 10 points off your test grade. However, no late tests will be allowed after I hand the graded tests back in class. If you miss a test, you must try to take it during this &ldquolate&rdquo period. If you do not take the test during that period, you will receive a 0 for that grade. In that case, you will need to take the make-up exam to replace that 0.

Grades will be assigned as follows:

90% or better and a grade of at least 80% on the final

80% - 89% and a grade of at least 70% on the final

70% - 79% and a grade of at least 60% on the final

Withdrawn by student or instructor prior to last withdrawal date on school calendar

Incomplete grades (I) will be given only in very rare circumstances. Generally, to receive a grade of "I", a student must have taken all tests, be passing, and after the last date to withdraw, have a personal tragedy occur which prevents course completion. An incomplete grade cannot be carried beyond the established date in the following semester. The completion date is determined by the instructor but may not be later than the final deadline for withdrawal in the subsequent semester.

Attendance is required in this course. It is extremely important for you to attend class regularly. I MAY drop you from the course for excessive absences, although I make no commitment to do so.

It is the student's responsibility to initiate all withdrawals in this course. The instructor may withdraw students for excessive absences (4) but makes no commitment to do this for the student. After the last day to withdraw, neither the student nor the instructor may initiate a withdrawal. It is the responsibility of each student to ensure that his or her name is removed from the roll should he or she decide to withdraw from the class. The instructor does, however, reserve the right to drop a student should he or she feel it is necessary. The student is also strongly encouraged to retain a copy of the withdrawal form for their records.

Students who enroll for the third or subsequent time in a course taken since Fall, 2002, may be charged a higher tuition rate, for that course. State law permits students to withdraw from no more than six courses during their entire undergraduate career at Texas public colleges or universities. With certain exceptions, all course withdrawals automatically count towards this limit. Details regarding this policy can be found in the ACC college catalog.

The withdrawal deadline for

**Spring 2019**is.__April 29, 2019__Please, try to keep up with the homework and with the lecture in class. There just isn't much time to catch up. This means you have to be sure to allow yourself plenty of time to do the homework and to study.

Classroom behavior should support and enhance learning. Behavior that disrupts the learning process will be dealt with appropriately, which may include having the student leave class for the rest of that day. In serious cases, disruptive behavior may lead to a student being withdrawn from the class. ACC's policy on student discipline can be found in the Student Handbook on the web at: http://www.austincc.edu/handbook

All students are expected to actively participate in this class. This can include asking relevant questions in class, participating in class discussions and other in-class activities, helping other students, coming to office hours with questions, and doing other things that contribute to the class.

Please, please, please, if you don't understand something, or you aren't clear about something, or if you think I (or the book) have made a mistake (it has been known to happen), or if you have any other questions, please ask. Don't let confusion accumulate. If you don't want to ask in class, come to our office hours (or call) and ask. It is much easier to ask a question now than to miss it on the test. I expect all students to participate in class discussions and other activities. Trust me, you will get much more out of the class if you become actively involved in it.

**Always show your work:**It is much more important that you understand the processes involved in solving problems than that you just give me the right answer. If I see from your work that you understand what you are doing, I will usually give partial credit for a problem, even if you made a mistake somewhere along the line. If you don't show your work (unless I believe you could reasonably do it in your head), I may not give you full credit, even if the answer is right. If you can really do something in your head, that's great, but when in doubt, write it down. It is also very important that you write what you mean. I will correct your notation the first few times, but I will start counting it wrong if you continue to write things incorrectly. In addition, please write clearly and legibly. If I can't read it, I won't grade it.

**Time required and outside help:**To do homework and study requires two or three times as much time outside of class as the time you spend in class in order to succeed in this course. If you need more out-of-class help than you can obtain in your instructor's office hours, free tutoring is available in any of ACC's Learning Labs.

ACC main campuses have Learning Labs which offer free first-come, first-serve tutoring in mathematics courses. The locations, contact information and hours of availability of the Learning Labs are posted at: http://www.austincc.edu/tutor

**COURSE OBJECTIVES/LEARNING OUTCOMES:**

**Course Objectives for MATH 2413:**1. Find limits of functions (graphically, numerically and algebraically)

2. Analyze and apply the notions of continuity and differentiability to algebraic and transcendental functions.

3. Determine derivatives by a variety of techniques including explicit differentiation, implicit differentiation, and logarithmic differentiation. Use these derivatives to study the characteristics of curves. Determine derivatives using implicit differentiation and use to study characteristics of a curve.

4. Construct detailed graphs of nontrivial functions using derivatives and limits.

5. Use basic techniques of integration to find particular or general antiderivatives.

6. Demonstrate the connection between area and the definite integral.

7. Apply the Fundamental theorem of calculus to evaluate definite integrals.

8. Use differentiation and integration to solve real world problems such as rate of change, optimization, and area problems.

**Student Learning Outcomes for MATH 2413:**Upon successful completion of this course, students will:

1. Solve tangent and area problems using the concepts of limits, derivatives, and integrals.

2. Draw graphs of algebraic and transcendental functions considering limits, continuity, and differentiability at a point.

3. Determine whether a function is continuous and/or differentiable at a point using limits.

4. Use differentiation rules to differentiate algebraic and transcendental functions.

5. Identify appropriate calculus concepts and techniques to provide mathematical models of real-world situations and determine solutions to applied problems.

6. Evaluate definite integrals using the Fundamental Theorem of Calculus.

7. Demonstrate an understanding of the relationship between derivatives and integrals using the Fundamental Theorem of Calculus.

**The General Education Competency of:**1. Critical Thinking: gathering, analyzing, synthesizing, evaluating and applying information is covered in every SLO.

2. Quantitative and Empirical Reasoning: applying mathematical, logical, and scientific principles and methods is covered in every SLO.

3. Technology Skills: using appropriate technology to retrieve, manage, analyze, and present information is covered in SLOs # 1, 2, 3, 5, and 7.

4. Written, Oral and Visual Communication: communicating effectively adapting to purpose, structure, audience and medium is covered in every SLO.

__ACC College Policies__**Statement on Scholastic Dishonesty -**A student attending ACC assumes responsibility for conduct compatible with the mission of the college as an educational institution. Students have the responsibility to submit coursework that is the result of their own thought, research, or self-expression. Students must follow all instructions given by faculty or designated college representatives when taking examinations, placement assessments, tests, quizzes, and evaluations. Actions constituting scholastic dishonesty include, but are not limited to, plagiarism, cheating, fabrication, collusion, and falsifying documents. Penalties for scholastic dishonesty will depend upon the nature of the violation and may range from lowering a grade on one assignment to an &ldquoF&rdquo in the course and/or expulsion from the college. See the Student Standards of Conduct and Disciplinary Process and other policies at http://www.austincc.edu/current/needtoknow**Student Rights and Responsibilities -**Students at the college have the rights accorded by the U.S. Constitution to freedom of speech, peaceful assembly, petition, and association. These rights carry with them the responsibility to accord the same rights to others in the college community and not to interfere with or disrupt the educational process. Opportunity for students to examine and question pertinent data and assumptions of a given discipline, guided by the evidence of scholarly research, is appropriate in a learning environment. This concept is accompanied by an equally demanding concept of responsibility on the part of the student. As willing partners in learning, students must comply with college rules and procedures.**Statement on Students with Disabilities -**Each ACC campus offers support services for students with documented disabilities. Students with disabilities who need classroom, academic or other accommodations must request them through Student Accessibility Services (SAS, formerly OSD). Students are encouraged to request accommodations when they register for courses or at least three weeks before the start of the semester, otherwise the provision of accommodations may be delayed.Students who have received approval for accommodations from SAS for this course must provide the instructor with the &lsquoNotice of Approved Accommodations&rsquo from SAS before accommodations will be provided. Arrangements for academic accommodations can only be made after the instructor receives the &lsquoNotice of Approved Accommodations&rsquo from the student.

Students with approved accommodations are encouraged to submit the &lsquoNotice of Approved Accommodations&rsquo to the instructor at the beginning of the semester because a reasonable amount of time may be needed to prepare and arrange for the accommodations. Additional information about Student Accessibility Services is available at HYPERLINK "http://www.austincc.edu/support/osd/" http://www.austincc.edu/support/osd/

**Safety Statement -**Austin Community College is committed to providing a safe and healthy environment for study and work. You are expected to learn and comply with ACC environmental, health and safety procedures and agree to follow ACC safety policies. Additional information on these can be found at http://www.austincc.edu/ehs . Because some health and safety circumstances are beyond our control, we ask that you become familiar with the Emergency Procedures poster and Campus Safety Plan map in each classroom. Additional information about emergency procedures and how to sign up for ACC Emergency Alerts to be notified in the event of a serious emergency can be found at http://www.austincc.edu/emergency/ .Please note, you are expected to conduct yourself professionally with respect and courtesy to all. Anyone who thoughtlessly or intentionally jeopardizes the health or safety of another individual will be dismissed from the day&rsquos activity, may be withdrawn from the class, and/or barred from attending future activities.

You are expected to conduct yourself professionally with respect and courtesy to all. Anyone who thoughtlessly or intentionally jeopardizes the health or safety of another individual will be immediately dismissed from the day&rsquos activity, may be withdrawn from the class, and/or barred from attending future activities.

**Communication with your Instructor -**All e-mail communication to students will be sent solely to the student&rsquos ACCmail account or math software if applicable, with the expectation that such communications will be read in a timely fashion. Likewise, students should use their ACCmail account or math software when communicating with instructors. Instructors will respond to student emails within 3 business days, if no response has been received by the student at the end of that time, then the student should send a reminder to the instructor.**Testing Center Policy -**Under certain circumstances, an instructor may have students take an examination in a testing center. Students using the Academic Testing Center must govern themselves according to the Student Guide for Use of ACC Testing Centers and should read the entire guide before going to take the exam. To request an exam, one must have:· Course Abbreviation (e.g., ENGL)

Do NOT bring cell phones to the Testing Center. Having your cell phone in the testing room,

**regardless of whether it is on or off**, will revoke your testing privileges for the remainder of the semester. ACC Testing Center policies can be found at http://www.austincc.edu/testctr/**Student And Instructional Services -**ACC strives to provide exemplary support to its students and offers a broad variety of opportunities and services. Information on these services and support systems is available at: http://www.austincc.edu/s4/ Links to many student services and other information can be found at: http://www.austincc.edu/current/ For help setting up your ACCeID, ACC Gmail, or ACC Blackboard, see a Learning Lab Technician at any ACC Learning Lab.**Concealed Handgun Policy -**The Austin Community College District concealed handgun policy ensures compliance with Section 411.2031 of the Texas Government Code (also known as the Campus Carry Law), while maintaining ACC&rsquos commitment to provide a safe environment for its students, faculty, staff, and visitors. Beginning August 1, 2017, individuals who are licensed to carry (LTC) may do so on campus premises except in locations and at activities prohibited by state or federal law, or the college&rsquos concealed handgun policy. It is the responsibility of license holders to conceal their handguns at all times. Persons who see a handgun on campus are asked to contact the ACC Police Department by dialing 222 from a campus phone or 512-223-7999. Refer to the concealed handgun policy online at austincc.edu/campuscarry .**Student Support Services -**Resources to support you are available at every campus. Food pantries are available at all campus Student Life offices (https://sites.austincc.edu/sl/programs/foodpantry/). Assistance paying for childcare or utility bills is available at any campus Support Center (http://www.austincc.edu/students/support-center). For sudden, unexpected expenses that may cause you to withdraw from one or more of your courses, go to http://www.austincc.edu/SEF to request emergency assistance through the Student Emergency Fund. Help with budgeting for college and family life is available through the Student Money Management Office (http://sites.austincc.edu/money/). Counselors are available at any campus if you experience a personal or mental health concern (http://www.austincc.edu/students/counseling). All services are free and confidential.**Course Outline and Approximate Calendar:**

Please note: schedule changes may occur during the semester.

Any changes will be announced in class.

## Watch the video: Mathematica vs. Python (November 2021).