Program Overview

Mathematical Sciences (MAT) Program

The Mathematical Sciences (MAT) program at DePaul University offers a comprehensive curriculum that covers various aspects of mathematics, including pure and applied mathematics, statistics, and mathematics education.

Program Overview

The MAT program provides students with a strong foundation in mathematical concepts, theories, and applications. The program is designed to prepare students for careers in mathematics, statistics, education, and related fields.

Course Descriptions

The program offers a wide range of courses, including:

• MAT 94: Basic Algebra - The objective of this course is to increase the students' competence in working with ordinary arithmetic, using a large variety of practical problems and situations from basic sciences as motivation.
• MAT 95: Introductory Algebra - An introduction to functions, linear equations, linear inequalities, absolute values, systems of linear equations, exponents, and polynomials.
• MAT 100: Introduction to Quantitative Reasoning - An introduction to the algebra needed for quantitative reasoning with a focus on functions and modeling.
• MAT 101: Intermediate Algebra - Functions, factoring, rational expressions, roots, radicals, quadratic equations, quadratic inequalities.
• MAT 110: Foundations of Mathematics for Elementary School Teachers I - This course gives students a deeper understanding of the foundations of elementary mathematics.
• MAT 111: Foundations of Mathematics for Elementary School Teachers II - This course gives students a deeper understanding of the foundations of elementary mathematics.
• MAT 112: Gambling and Games, Probability and Statistics - Students with very little mathematical background and little or no computing background will be given a brief introduction to the use of Microsoft Excel for mathematical purposes.
• MAT 115: Mathematics for Elementary School Teachers III - Continuation of Math 110-111.
• MAT 120: Quantitative Reasoning - This course provides a mathematical foundation for students to become confident and critical users of quantitative information of all kinds: numerical, graphical, and verbal.
• MAT 130: Functions and Mathematical Models - Functions and their graphs, modeling with linear and quadratic functions, polynomial and rational functions, inverse functions, exponential and logarithmic functions.
• MAT 131: Precalculus and Trigonometry - Functions and their graphs, inverse functions, exponential and logarithmic functions, polynomial and rational functions, trigonometric functions, inverse trigonometric functions.
• MAT 135: Business Calculus I - Differential calculus of one or more variables with business applications.
• MAT 136: Business Calculus II - Integral calculus, matrix algebra, and probability theory with business applications.
• MAT 137: Business Statistics - Basic concepts of statistics and applications; data analysis with the use of Excel; theoretical distributions; sampling distributions; problems of estimation; hypothesis testing.
• MAT 140: Discrete Mathematics I - Combinatorics, graph theory, propositional logic, singly-quantified statements, operational knowledge of set theory, functions, number systems, methods of direct and indirect proof.
• MAT 141: Discrete Mathematics II - Methods of direct and indirect proof, set theoretic proofs, sequences, mathematical induction, recursion, multiply-quantified statements, relations and functions, complexity.
• MAT 147: Calculus with Integrated Precalculus I - Limits, continuity, the derivative, rules of differentiation, derivatives of trigonometric and logarithmic functions and their inverses, applications, with precalculus review included for each topic.
• MAT 148: Calculus with Integrated Precalculus II - Extrema, curve sketching, related rates, definite and indefinite integrals, applications of the integral, with precalculus review included for each topic.
• MAT 149: Calculus with Integrated Precalculus III - Techniques of integration, L'Hopital's rule, improper integrals, Taylor polynomials, series and sequences, first-order differential equations, with precalculus review included for each topic.
• MAT 150: Calculus I - Limits, continuity, the derivative, rules of differentiation, derivatives of trigonometric and logarithmic functions and their inverses, applications of the derivative, extrema, curve sketching, and optimization.
• MAT 151: Calculus II - Definite and indefinite integrals, the Fundamental Theorem of Calculus, applications of the integral, techniques of integration.
• MAT 152: Calculus III - L'Hopital's rule, improper integrals, sequences and series, Taylor polynomials.
• MAT 155: Summer Calculus I - Limits, continuity, the derivative, rules of differentiation, derivatives of trigonometric and logarithmic functions and their inverses, applications of the derivative, extrema, curve sketching, and optimization.
• MAT 156: Summer Calculus II - Further applications of the integral, techniques of integration, L'Hopital's rule, improper integrals, sequences and series, Taylor polynomials.
• MAT 160: Calculus for Mathematics and Science Majors I - Limits, continuity, the derivative, rules of differentiation, derivatives of trigonometric and logarithmic functions and their inverses, applications of the derivative, extrema, curve sketching, and optimization.
• MAT 161: Calculus for Mathematics and Science Majors II - Definite and indefinite integrals, the Fundamental Theorem of Calculus, applications of the integral, techniques of integration.
• MAT 162: Calculus for Mathematics and Science Majors III - L'Hopital's rule, improper integrals, sequences and series, Taylor polynomials.
• MAT 170: Calculus for Life Sciences I - The course covers the following topics using examples from the sciences: Functions as models, logarithmic scale graphing, exponential growth and decay, difference equations and limits of sequences.
• MAT 171: Calculus for Life Sciences II - The course covers the following topics using examples from the sciences: Applications of the derivative including approximation and local linearity, differentials, extrema and the Mean Value Theorem.
• MAT 172: Calculus III with Differential Equations - This course is designed for students in the life sciences and covers some topics from MAT 152, differential equations and an introduction to the Calculus of functions of several variables.
• MAT 207: History of Probability and Statistics - History Of Probability And Statistics.
• MAT 215: Introduction to Mathematical Reasoning - An introduction to basic concepts and techniques used in higher mathematics courses: set theory, equivalence relations, functions, cardinality, techniques of proof in mathematics.
• MAT 216: Foundations of Advanced Mathematics - Introduction to abstract mathematics: congruences, modular arithmetic, the Euclidean algorithm, proofs involving manipulation of inequalities and estimation, sequences and their limits.
• MAT 220: Applied Linear Algebra - Systems of linear equations, matrices and matrix algebra, determinants, diagonalization and matrix factorization with MATLAB/Maple, with applications to linear programming and graph theory.
• MAT 242: Elements of Statistics - Descriptive statistics, elements of probability, the binomial and normal probability models; large and small sample hypothesis testing, correlation and regression analysis.
• MAT 260: Multivariable Calculus I - Vectors, dot and cross products, parameterizations of lines and planes in space, functions of several independent variables, partial derivatives, tangent planes and linear approximations.
• MAT 261: Multivariable Calculus II - Surface areas, triple integrals, vector functions and space curves, derivatives of vector functions, arc length and curvature, vector fields, line integrals, Green's Theorem.
• MAT 262: Linear Algebra - Systems of linear equations and matrices; vectors in n-space; vector spaces: linear combinations, linear independence, basis; linear transformations, change of basis, eigenvalues and eigenvectors.
• MAT 301: History of Mathematics - History of mathematics with problem solving.
• MAT 302: Combinatorics - Methods of counting and enumeration of mathematical structures.
• MAT 303: Theory of Numbers - A study of properties of integers: divisibility; Euclid's Algorithm; congruences and modular arithmetic; Euler's Theorem; Diophantine equations; distribution of primes; RSA cryptography.
• MAT 304: Differential Equations - Linear equations, systems with constant coefficients, series solutions, Laplace transforms, and applications.
• MAT 309: Teaching and Learning Secondary School Mathematics - Theories, methods, and materials for teaching and learning mathematics in secondary schools.
• MAT 310: Abstract Algebra I - The first quarter of a 3-quarter sequence.
• MAT 311: Abstract Algebra II - A continuation of topics from MAT 310: Groups, rings, fields, polynomial rings, isomorphism theorems, extension fields, and an introduction to Galois theory.
• MAT 312: Abstract Algebra III - A continuation of topics from MAT 311: Groups, rings, fields, polynomial rings, isomorphism theorems, extension fields, and an introduction to Galois theory.
• MAT 320: Geometry I - Incidence and separation properties of planes; congruences; the parallel postulate; area theory; ruler and compass construction.
• MAT 321: Geometry II - Introduction to solid geometry and noneuclidean geometry (hyperbolic and spherical models); other special topics.
• MAT 323: Data Analysis and Statistical Software I - Computing with a statistical package.
• MAT 324: Data Analysis & Statistical Software II - Advanced features and applications of the statistical package used in MAT 323.
• MAT 326: Sample Survey Methods - Simple random, stratified, systematic and cluster sampling.
• MAT 328: Design of Experiments - Linear models and quadratic forms.
• MAT 330: Methods of Computation and Theoretical Physics I - Computational and theoretical methods in ordinary differential equations, complex numbers, systems of equations, phase plane analysis, and bifurcations.
• MAT 331: Methods of Computation and Theoretical Physics II - Computational and theoretical methods in ordinary differential equations, complex numbers, systems of equations, phase plane analysis, and bifurcations.
• MAT 335: Real Analysis I - Real number system, completeness, supremum, and infimum, sequences and their limits, lim inf, lim sup, limits of functions, continuity.
• MAT 336: Real Analysis II - Properties of continuous functions, uniform continuity, sequences of functions, differentiation, integration.
• MAT 337: Complex Analysis - Complex functions; complex differentiation and integration; series and sequences of complex functions.
• MAT 340: Topology - An introduction to point-set topology: metric spaces, topological spaces, continuity, connectedness, and compactness.
• MAT 341: Statistical Methods Using SAS - The SAS programming language.
• MAT 342: Elements of Statistics II - Multiple regression, correlation, analysis of variance, time series, and sampling.
• MAT 343: Business Statistics II - Multiple regression, correlation, analysis of variance, time series and sampling.
• MAT 348: Applied Statistical Methods - Introduction to statistical software (which will be used throughout the course).
• MAT 349: Applied Probability - Probability theory, probability distributions, mathematical expectation, functions of random variables, sampling distributions, estimation, tests of hypotheses, simulation.
• MAT 350: Bayesian Statistics - Comparison of Bayesian and frequentist methods, conditional probability, Bayes theorem, conjugate distributions, computational methods, hands-on Bayesian data analysis using appropriate software.
• MAT 351: Probability and Statistics I - The course covers elements of probability theory, distributions of random variables and linear functions of random variables, moment generating functions, and discrete and continuous probability models.
• MAT 352: Probability and Statistics II - A continuation of MAT 351.
• MAT 353: Probability and Statistics III - A continuation of MAT 352.
• MAT 354: Multivariate Statistics - The multivariate normal distribution.
• MAT 355: Stochastic Processes - Discrete Markov chains and random walks, birth and death processes, Poisson processes, queuing systems, and renewal processes.
• MAT 356: Applied Regression Analysis - Simple linear, multiple, polynomial and general linear regression models.
• MAT 357: Nonparametric Statistics - Inference concerning location and scale parameters, goodness of fit tests, association analysis and tests of randomness using distribution free procedures.
• MAT 358: Applied Time Series and Forecasting - Development of the Box-Jenkins methodology for the identification, estimation, and fitting of ARIMA, and transfer-function stochastic models.
• MAT 359: Simulation Models and Monte Carlo Method - Techniques of computer simulation of the classical univariate and multivariate probability distribution models.
• MAT 360: Generalized Linear Models - Applications of generalized linear models.
• MAT 361: Theory of Interest - Theory and applications of compound interest to annuities, amortization schedules, sinking funds, bonds, and yield rates.
• MAT 362: Life Contingencies I - Basic Contingencies: The theory and applications of contingency mathematics in life and health insurance, annuities, and pensions.
• MAT 363: Life Contingencies II - Advanced Contingencies: A continuation of Mathematics 362.
• MAT 364: Loss Models I - Severity and frequency models, aggregate models, coverage modifications, risk measures, construction and selection of parametric models.
• MAT 365: Loss Models II - Bayesian credibility, Buhlmann credibility, insurance and reinsurance coverages, pricing and reserving.
• MAT 366: Mathematical Demography - Introduction to demography; mortality table construction and methods of population and demographic analysis.
• MAT 367: Credibility Theory - Credibility theory and loss distributions with applications to casualty insurance classification and ratemaking.
• MAT 368: Mathematics for Finance - The course covers the mathematics of financial derivatives, investment strategies, arbitrage, put-call parity, binomial models for European options and interest rates.
• MAT 369: Actuarial Science Seminar - This course is a problem solving seminar that covers relevant topics in probability and statistics in the first actuarial exam: Exam P/1.
• MAT 370: Advanced Linear Algebra - Vector spaces, basis and dimension; matrix representation of linear transformations and change of basis; diagonalization of linear operators; inner product spaces.
• MAT 372: Logic and Set Theory - Topics in axiomatic set theory, formal logic, and computability theory.
• MAT 381: Fourier Analysis and Special Functions - The course covers the basic principles of discrete and continuous Fourier analysis and some of its applications currently used in scientific modeling.
• MAT 384: Mathematical Modeling - Modeling of real world problems using mathematical methods.
• MAT 385: Numerical Analysis I - Use of a digital computer for numerical computation.
• MAT 386: Numerical Analysis II - Theory and algorithms for efficient computation including the Fast Fourier Transform.
• MAT 387: Operations Research: Linear Programming - Linear programming, integer programming and LP relaxation, the duality theorem, simplex algorithm, interior point methods, applications to industrial engineering.
• MAT 388: Operations Research: Optimization Theory - Convex optimization, quadratic optimization problems, Lagrange multipliers and generalization to inequality constraints.
• MAT 389: Topics in Operations Research - Advanced topics in operations research and optimization theory.
• MAT 390: Mathematics Reading and Research - The course provides students with a hands-on experience about research in mathematical sciences.
• MAT 391: Studies in Demography - The course introduces students to the study by statistical methods of human populations in terms of type of data sources, population composition, growth, fertility, mortality, morbidity, health, migration, and urbanization.
• MAT 395: Topics in Mathematics - Consult course schedule for current offerings.
• MAT 396: Senior Thesis Research - A thesis option is available to mathematics majors who wish to pursue an extended independent project related to a theoretical or applied focus of the program.
• MAT 397: Mathematical Pedagogy: Theory & Practice - Introduction to current theories and practices in college mathematics instruction.
• MAT 398: Senior Capstone Seminar - Topics vary from year to year.
• MAT 399: Independent Study - (variable credit)
• MAT 400: Applied Abstract Algebra I - Applied Abstract Algebra I.
• MAT 401: Applied Abstract Algebra II - Applied Abstract Algebra II.
• MAT 421: Basic Biostatistics - This course includes both data analysis and experimental design, up to and including survival analysis such as used in the analysis of clinical trials.
• MAT 424: Advanced Biostatistics - The overall objective is the development of statistical literacy and skills in the analysis of biological and medical data including: generalized linear models, analysis of repeated measures, log-linear models, clinical trials and computer applications.
• MAT 425: Survival Analysis - Basic quantities and models in survival analysis, types of censoring and truncation data, estimation for various survival models, nonparametric estimation of hazard and survival functions.
• MAT 426: Generalized Linear Models - Applications of generalized linear models.
• MAT 427: Bayesian Statistics - Comparison of Bayesian and frequentist methods, conditional probability, Bayes theorem, conjugate distributions, computational methods, hands-on Bayesian data analysis using appropriate software.
• MAT 434: Topology - An introduction to point-set topology: metric spaces, topological spaces, continuity, connectedness, and compactness.
• MAT 435: Measure Theory - This is a course in Lebesgue integration; the study of measure spaces and measurable functions; the basic theorems of Lebesque integration.
• MAT 436: Functional Analysis - This course is an introduction to the basic theory of functional analysis.
• MAT 437: Complex Analysis - Complex functions; complex differentiation and integration; series and sequences of complex functions.
• MAT 441: Applied Statistics I - Parametric and non-parametric statistical inferential methods for the univariate and bivariate situations using SAS and R.
• MAT 442: Applied Statistics II - A continuation of MAT 441.
• MAT 443: Applied Statistics III - A continuation of MAT 442.
• MAT 448: Statistical Methods Using SAS - The SAS programming language.
• MAT 449: Statistical Data Management - Students learn data organization and structures, design of statistical databases, statistical software analysis.
• MAT 450: Advanced Statistical Computing - Advanced statistical computing methods used in modern scientific investigation.
• MAT 451: Probability and Statistics I - The course covers elements of probability theory, distributions of random variables and linear functions of random variables, moment generating functions, and discrete and continuous probability models.
• MAT 452: Probability and Statistics II - A continuation of MAT 451.
• MAT 453: Probability and Statistics III - A continuation of MAT 452.
• MAT 454: Multivariate Statistics - The multivariate normal distribution.
• MAT 455: Stochastic Processes - Discrete Markov chains and random walks, birth and death processes, Poisson processes, queuing systems, and renewal processes.
• MAT 456: Applied Regression Analysis - Simple linear, multiple, polynomial and general linear regression models.
• MAT 457: Nonparametric Statistics - Inference concerning location and scale parameters, goodness of fit tests, association analysis and tests of randomness using distribution free procedures.
• MAT 458: Statistical Quality Control - History; Deming guide to quality; graphical techniques of process control; Schewhart's control charts for means, ranges, standard deviations, individual measurements, and attributes.
• MAT 459: Simulation Models and Monte Carlo Method - Techniques of computer simulation of the classical univariate and multivariate probability models.
• MAT 460: Topics in Statistics - One of the following topics: Clinical trials; Reliability and life testing; Categorical data analysis; Bootstrapping; Data Mining; Response Surface Methodology; Meta analysis; Survival Models.
• MAT 461: Actuarial Science I: Theory of Interest - Theory and application of compound interest to annuities, amortization schedules, sinking funds, bonds, and yield rates.
• MAT 462: Actuarial Science II: Basic Contingencies - Basic Contingencies: The theory and applications of contingency mathematics in life and health insurance annuities and pensions.
• MAT 463: Actuarial Science III: Advanced Contingencies - Advanced Contingencies: A continuation of MAT 462.
• MAT 464: Loss Models I - Severity and frequency models, aggregate models, coverage modifications, risk measures, construction and selection of parametric models.
• MAT 465: Loss Models II - Bayesian credibility, Buhlmann credibility, insurance and reinsurance coverages, pricing and reserving.
• MAT 466: Mathematical Demography - Introduction to demography, mortality table construction and methods of population and demographic analysis.
• MAT 467: Credibility Theory - Credibility theory and loss distributions with applications to casualty insurance classification and ratemaking.
• MAT 468: Mathematics for Finance - The course covers the mathematics of financial derivatives, investment strategies, arbitrage, put-call parity, binomial models for European options and interest rates.
• MAT 469: Stochastic Calculus - The course introduces students to the mathematical tools and techniques used in modern Financial Theory.
• MAT 470: Advanced Linear Algebra - Vector spaces and subspaces, basis and dimension; matrix representation of linear transformations and change of basis; null spaces and ranges; dual spaces; eigenvalues, eigenvectors, and diagonalization.
• MAT 471: Group Theory - Classes of groups; actions of groups on sets; Sylow theorems; decomposition of groups; structure of finite abelian groups.
• MAT 472: Fields and Galois Theory - Commutative rings and fields; irreducible polynomials and field extensions, adjunction of roots, algebraic extensions, splitting and normal fields, cyclic extensions, the Galois group, and the Fundamental theorem of Galois theory.
• MAT 473: Rings and Modules - Rings and Algebras; classes of unique factorization domains; modules and principal isomorphism theorems, classes of modules, decomposition of finitely generated modules.
• MAT 481: Fourier Analysis and Special Functions - The course covers the basic principles of discrete and continuous Fourier analysis and its applications.
• MAT 482: Partial Differential Equations - Introduction to partial differential equations and their applications.
• MAT 484: Mathematical Modeling - Modeling of real world problems using mathematical methods.
• MAT 485: Numerical Analysis I - Use of a digital computer for numerical computation.
• MAT 486: Numerical Analysis II - Theory and algorithms for efficient computation including the Fast Fourier Transform.
• MAT 487: Operations Research: Linear Programming - Linear programming, integer programming and LP relaxation, the duality theorem, simplex algorithm, interior point methods, applications to industrial engineering.
• MAT 488: Operations Research: Optimization Theory - Convex optimization, quadratic optimization problems, Lagrange multipliers and generalization to inequality constraints.
• MAT 489: Queuing Theory with Applications - Discrete and continuous-time Markov chain models, Queuing systems, and topics from renewal and reliability theory.
• MAT 491: Data Mining - This course will provide students with methodologies of mining varied data and discovering knowledge from data.
• MAT 494: Graph Theory - This course studies graph theory and its applications.
• MAT 495: Dynamic Programming - Optimization of sequential decision processes.
• MAT 496: Game Theory - The minimax theorem for two-person, zero-sum games.
• MAT 498: Problem Solving in Mathematics - Course topics: problem solving in various topics from GRE Subject examination in Mathematics.
• MAT 512: Applied Time Series and Forecasting - Development of the Box-Jenkins methodology for the identification, estimation, and fitting of ARIMA, and transfer-function stochastic models.
• MAT 515: Financial Modeling - The course expounds on probabilistic methods used in risk-based capital allocation and risk management.
• MAT 526: Sampling Theory and Methods - Simple random, stratified, systematic and cluster sampling.
• MAT 528: Design and Analysis of Experiments - Single-factor fixed, random and mixed designs with and without restrictions on randomizations.
• MAT 595: Graduate Thesis Research - A thesis option is available to graduate students who wish to pursue an extended independent project.
• MAT 596: Advanced Topics in Algebra - Consult course schedule for current offerings.
• MAT 597: Advanced Topics in Analysis - Consult course schedule for current offerings.
• MAT 598: Advanced Problem Solving in Algebra and Analysis - Course topics: problem solving in various topics in Algebra and Analysis.
• MAT 599: Independent Study - Offered by arrangement.
• MAT 600: Experimentation, Conjecture, and Reasoning with Numbers - This course will focus on furthering the participants' number sense together with providing them with opportunities to use and discuss the roles of experimentation, conjecture, and logical reasoning.
• MAT 605: Geometry for Middle School Teachers - An introduction to geometry designed to engage students in the construction, description, and analysis of geometric objects.
• MAT 608: Investigating High School Mathematics - Drawing on high school mathematics content, students will identify and explore the mathematical themes that might form the content of a 12th grade capstone course.
• MAT 609: Teaching and Learning Secondary School Mathematics - Theories, methods, materials and techniques for teaching and learning mathematics in secondary and upper elementary schools.
• MAT 610: Calculus I - A review of topics from precalculus using algebraic, numerical, and graphical perspectives.
• MAT 611: Calculus II - A continuation of Math 610.
• MAT 612: Calculus III - A continuation of Math 611.
• MAT 618: Topics in Calculus and Differential Equations - Taylor series and Taylor's theorem, parametric equations, separable differential equations, slope fields, Euler's method.
• MAT 620: Geometry - Axiom systems, types of reasoning used in proofs, Euclidean geometry results with concentration on triangles and circles.
• MAT 621: Transition to Algebra for Middle School Teachers - In this course, teachers will begin the study of algebra as a generalization of number and operation.
• MAT 622: Algebra for Middle School Teachers I - This course is the first of a 3-quarter sequence designed in part to prepare elementary and middle grade teachers to teach an algebra class to qualified 8th grade students.
• MAT 623: Algebra for Middle School Teachers II - The second course in the algebra sequence builds on the first and maintains emphases on problem-solving, deeper understanding of the central concepts of beginning algebra.
• MAT 624: Functions and Modeling - Advanced concepts in beginning algebra provide a basis for a deeper treatment of the relationship between functions and data.
• MAT 631: History of Mathematics through Problem Solving - Topics include the development of calculus, probability theory, number theory, non-Euclidean geometry, and set theory.
• MAT 632: History and Cultural Foundations of Mathematics - This course is a cross-cultural survey of the history of mathematics, with emphasis placed on the development of concepts encountered by students in elementary and middle school.
• MAT 640: Multivariable Calculus I - Functions of several variables, vectors, dot products and cross products, partial differentiation, directional derivatives, optimization, Lagrange multipliers.
• MAT 641: Multivariable Calculus with Linear Algebra for Mathematics Teachers - Multiple integration, line and surface integrals, change of variable in multiple integration, Green's and Stokes' theorems.
• MAT 642: Multivariable Calculus II - Double and iterated integrals, area by double integrals, triple integrals, triple integrals in cylindrical and spherical coordinates.
• MAT 643: Ideas of Calculus in the Middle School Curriculum - The course will introduce students to the "big ideas" of Calculus including limits, derivatives, and integrals.
• MAT 644: Differential Equations - This course will continue the study of differential equations (DEs) begun in MAT 618.
• MAT 649: Data Analysis and Probability - This course covers the fundamental concepts of probability that are part of the middle school curriculum.
• MAT 650: Probability & Statistics for Mathematics Teachers I - Combinatorics, sets, probability, random variables, distribution and density functions, multiple integration, standard probability laws.
• MAT 651: Probability & Statistics for Mathematics Teachers II - Central limit theorem, point and interval estimation of parameters, hypothesis testing, least squares and regression.
• MAT 660: Discrete Mathematics - Logic and techniques of proof, mathematical induction, sets and functions, relations, introduction to number theory and combinatorics.
• MAT 665: Discrete Structures with a Transition to Higher Mathematics - A transition to advanced courses having a greater emphasis on proof and abstraction.
• MAT 670: Abstract Algebra I - Examines the integers, prime numbers, the Euclidean algorithm, the uniqueness of prime factorization, equivalence relations, rational numbers, real numbers, and complex numbers.
• MAT 671: Abstract Algebra II - Examines modular arithmetic, the irreducibility of polynomials over different fields, criteria for solvability by radicals.
• MAT 672: Linear Algebra - Vector spaces, linear combinations, spanning sets, linear independence, basis, dimension, systems of linear equations, matrices, linear transformation, eigenvalues and eigenvectors.
• MAT 680: Real Analysis - Construction and properties of the real numbers.
• MAT 699: Topics in Mathematics for Teachers - Diverse topics in mathematical modeling or mathematical appreciation germane to the secondary school classroom.