UGRD > MATH

## Mathematics Courses

#### MATH 114QR Quantitative Reasoning +

**Description:**

This course covers the basic algebra and technological tools used in the social, physical and life sciences to analyze quantitative information. The emphasis is on real world, open-ended problems that involve reading, writing, calculating, synthesizing, and clearly reporting results. Topics include descriptive statistics, linear, and exponential models. Technology used in the course includes computers (spreadsheets, Internet) and graphing calculators. More Info

**Offered in:**#### MATH 115 College Algebra +

**Description:**

Designed primarily but not exclusively for students seeking a stronger foundation in algebra before taking MATH 129 or MATH 130. Topics include basic algebra concepts, linear equations and inequalities and inequalities, properties of functions, linear and quadratic functions, absolute value equations and inequalities, systems of equations. More Info

**Offered in:**#### MATH 115R College Algb-Reduced +

#### MATH 125 Introductory Statistics +

**Description:**

This course is a concept-driven introduction to statistics and statistical reasoning. It covers descriptive statistics, including histograms, the normal curve, and linear correlation and regression; probability sufficient to enable development of inferential statistics; and topics in statistical inference. The latter will include sampling theory, confidence intervals and their interpretation, tests of hypotheses, and chi-square tests. More Info

**Offered in:**#### MATH 129 Pre-Calculus for Management and Social Science Students +

**Description:**

This course teaches the algebraic and conceptual skills students need to master before they are ready for MATH 134 or MATH 135. The major part of the course then involves the application of linear, quadratic, and exponential models to problems in management and economics. More Info

**Offered in:**#### MATH 129R Mgt Precalc-Reduced +

#### MATH 130 Precalculus +

**Description:**

Preparation for first year calculus. Covers symmetry, graphs, functions, lines, parabolas and max-min problems, exponential and logarithm functions, exponential growth, and the trigonometric functions and their inverses. More Info

**Offered in:**#### MATH 130R Precalc-Reduced Crdt +

**Description:**

Preparation for first-year calculus for students who have received credit in a course which covered most (but not all) of the following topics: symmetry, graphs, functions, lines, parabolas and max-min problems, exponential and logarithm functions, exponential growth, and the trigonometric functions and their inverses. More Info

**Offered in:**#### MATH 134 Managerial Calculus +

**Description:**

A one-semester course in calculus, with particular emphasis on applications to economics and management. Topics covered include limits, continuity, derivatives, and integrals. More Info

**Offered in:**#### MATH 135 Survey of Calculus +

**Description:**

Calculus developed intuitively and applied to problems in biology, economics, psychology, and geometry. A course for non-physical science and non-mathematics majors. Suitable for some pre-medical programs. More Info

**Offered in:**#### MATH 135R Survey of Calculus - Reduced Credit +

**Description:**

Calculus developed intuitively for students who have received credit in a course which covered most (but not all) of the following topics: calculus applied to problems in biology, economics, psychology, and geometry. A course for non-physical science and non-mathematics majors. Suitable for some pre-medical programs. More Info

**Offered in:**#### MATH 140 Calculus I +

**Description:**

The first in the sequence of calculus courses for science and math majors. Topics include limits, continuity, derivatives and their applications, and definite and indefinite integrals with applications to geometric and physical problems. More Info

**Offered in:**#### MATH 140R Calculus I - Reduced Credit +

**Description:**

The first in the sequence of calculus courses for science and math majors who have received credit in a course which covered most (but not all) of the following topics: limits, continuity, derivatives and their applications, and definite and indefinite integrals with applications to geometric and physical problems. More Info

**Offered in:**#### MATH 141 Calculus II +

**Description:**

Continuation of MATH 140. Topics include transcendental functions, techniques of integration, applications of the integral, improper integrals, L'Hospital's rule, sequences, and series. Note: Because MATH 141 is the second part of a three-semester calculus sequence, it should be taken as soon as possible after MATH 140. More Info

**Offered in:**#### MATH 141R Calculus II - Reduced Credit +

**Description:**

Continuation of MATH 140 for students who have received credit in a course which covered most (but not all) of the following topics: transcendental functions, techniques of integration, applications of the integral, improper integrals, L'Hospital's rule, sequences, and series. More Info

**Offered in:**#### MATH 145 Calculus I for Life & Environmental Sciences +

**Description:**

This calculus course presents topics of calculus in the context of the life and environmental sciences. Topics include limits, continuity, derivatives and their applications, and definite and indefinite integrals with applications to geometric and physical problems. More Info

**Offered in:**#### MATH 145R Calculus I for Life and Environmental Sciences - Reduced Credits +

**Description:**

This calculus course presents topics of calculus in the context of the life and environmental sciences for students who have received credit in a course which covered most (but not all) of the following topics: limits, continuity, derivatives and their applications, and definite and indefinite integrals with applications to geometric and physical problems. More Info

**Offered in:**#### MATH 211L Engineering Mathematics +

**Description:**

In this course students will learn important math concepts and techniques they will need to study engineering topics such as circuit analysis, signal processing, electromagnetic fields and wavers, etc. Topics include complex numbers and functions. Laplace transform, Fourier series and transform, first and second order differential equations, partial differential equations, vector differential calculus, matrix algebra, and probability and statistics. For each of these topics, engineering applications will be emphasized, and when appropriate, numerical solutions will be introduced. More Info

**Offered in:**- TBA

#### MATH 240 Multivariable Calculus +

**Description:**

Differential and integral calculus of functions of several variables. Topics include Euclidean, polar, cylindrical, and spherical coordinates; dot product, cross-product, equations of lines and planes; continuity, partial derivatives, directional, gradient; optimization in several variables; multiple integrals, integrated integrals, change of coordinates, Jacobians, general substitution rule. More Info

**Offered in:**#### MATH 242 Multivariable and Vector Calculus +

**Description:**

Differential and integral calculus of functions of several variables and of vector fields. Topics include Euclidean, polar, cylindrical, and spherical coordinates; dot product, cross-product, equations of lines and planes; continuity, partial derivatives, directional derivatives, optimization in several variables; multiple integrals, iterated integrals, change of coordinates, Jacobians, general substitution rule; curves and surfaces, parametrizations, line integrals, surface integrals; gradient, circulation, flux divergence; conservative, solenoidal vector fields; scalar, vector potential; Green, Gauss, and Stokes theorems. Please note: Because MATH 242 is the final part of a three-semester calculus sequence, it should be taken as soon as possible after MATH 141. More Info

**Offered in:**#### MATH 242R Multivariable and Vector Calculus - Reduced Credit +

**Description:**

Curves and surfaces, parametrizations, line integrals, surface integrals; gradient, circulation, flux, divergence; conservative, solenoidal vector fields; scalar, vector potential; Green, Gauss, and Stokes theorems. More Info

**Offered in:**#### MATH 260 Linear Algebra +

**Description:**

This is an introductory class in Linear Algebra. Topics include basic algebraic operations of Matrices, Linear systems of equations, Gauss-Jordan elimination, subspaces, linear independence, bases, dimension, linear maps, determinants, orthogonality, orthogonalization process, eigenvalues and eigenvectors, as well as a brief discussion on abstract vector spaces. More Info

**Offered in:**#### MATH 265 Discrete Structures in Mathematics +

**Description:**

This course is an introduction to discrete structures in mathematics. Topics include, but are not limited to: basic combinatorial structures and analysis; elementary number theory; sequences and operations with sequences; graphs and trees; equivalence and partial orders. More Info

**Offered in:**#### MATH 270 Applied Ordinary Differential Equations +

**Description:**

A comprehensive study of the nature of ordinary differential equations. The course includes qualitative analysis of properties of solutions, as well as standard methods for finding explicit solutions to important classes of differential equations. It presents many applications, particularly for linear equations. More Info

**Offered in:**#### MATH 291 Mathematical Software. An introduction to computer assisted math modeling and problem solving +

**Description:**

The purpose of this course is to develop a basic skillset in using computer software to approach, analyze, and report on mathematical problems. Students will learn to work collaboratively to investigate both basic problems and advanced mathematical topics via simulation and numerical exploration, and they will prepare professional level reports which compile and communicate their results. The topics and their applications will be illustrated using computer algebra software (e.g. Sage), a modern programming language (e.g. Python), and document creation software (e.g. Latex). More Info

**Offered in:**#### MATH 309 Financial Mathematics +

**Description:**

This course is an introduction to the fundamental concepts of financial mathematics including annuities, stocks, bonds, and financial derivates. Students will learn how these concepts are applied in calculating present and accumulated values for various streams of cash flows, which will serve as a basis for future use in: reserving, valuation, pricing, asset/liability management, investment income, capital budgeting, and valuing contingent cash flows. More Info

**Offered in:**#### MATH 314 Introduction to Proofs: a Transition to Advanced Mathematics +

**Description:**

The course is designed to aid students in making the transition from calculus, differential equations and linear algebra to the more advanced and more abstract mathematics courses, such as abstract algebra and real analysis. The course will cover mathematical logic, mathematical proofs, mathematical induction, set theory, relations, functions, cardinality and applications of proofs in the study of such areas as number theory, calculus and group theory, as time permits. More Info

**Offered in:**#### MATH 320 Applied Discrete Mathematics +

**Description:**

An introduction to the mathematical structures and concepts used in computing: sets, mathematical induction, ordered sets, Boolean algebras, predicate calculus, trees, relations and lattice theory. Formal and informal theories and corresponding mathematical proofs are taught. More Info

**Offered in:**- TBA

#### MATH 345 Probability and Statistics +

**Description:**

Introduction to the fundamental ideas and techniques of probability theory. Topics covered: properties of probability, independence, conditional probability, discrete and continuous random variables, density and distribution function, expectation, variance, covariance, moments, correlation, joint distribution, marginal, some common distributions such as uniform, Bernoulli, binomial, exponential, Poisson and normal distribution, and the Central Limit Theorem. The course also introduces some basic ideas of statistical analysis, e.g. parameter estimation and hypothesis testing. More Info

**Offered in:**#### MATH 350 Applied Partial Differential Equations +

**Description:**

Applied Partial differential Equations is an introduction to the basic properties of partial differential equations and to some of the techniques that have been developed to analyze the solutions to these equations. The equations that describe the dynamics of waves, diffusion, flow and vibrations will be the main focus of this course. Initial value and boundary value problems of first and second-order equations will be considered. A geometric and analytic analysis of the solutions to these equations will be explored. Specific topics covered include classification of partial differential equations, well posed problems, the maximum principles for the diffusion equation and Laplace's equation, Dirichlet, Neumann and Robin boundary conditions, the method of characteristic coordinates, and separation of variables. The theory of Fourier Series will be introduced to the student and used to approximate solutions to inhomogeneous boundary value problems using the expansion method. Additional topics specific to the instructor's preference may be included in the course if time permits. More Info

**Offered in:**- TBA

#### MATH 358 An Introduction to Complex Analysis +

#### MATH 360 Abstract Algebra +

#### MATH 361 Abstract Algebra II +

**Description:**

Introduction to ring and field theory. Topics include: commutative rings, ideals, integral domains, polynomial fields, the theory of extension fields, vector spaces, Galois groups, and the fundamental theorem of Galois theory. Applications include insolvability of certain higher degree polynomials, and other topics as time permits. More Info

**Offered in:**#### MATH 370 History of Mathematics +

**Description:**

This course traces the development of mathematics from ancient times up to and including 17th century developments in the calculus. Emphasis is on the development of mathematical ideas and methods of problem solving. More Info

**Offered in:**#### MATH 380 Introduction to Computational Algebraic Geometry +

**Description:**

This course is an introduction to the geometry of affine algebraic varieties, with emphasis on the algebra-geometry dictionary and on computation via Groebner bases and Buchberger's algorithm. More Info

**Offered in:**- TBA

#### MATH 390 Mathematical Problem Solving Seminar +

**Description:**

This course is an undergraduate seminar on mathematical problem solving. It is intended for students who enjoy solving challenging mathematical problems and who are interested in learning various techniques and background information useful for problem solving. More Info

**Offered in:**#### MATH 425 Numerical Analysis +

**Description:**

This course provides an introduction to numerical analysis and its applications in practical problems in applied mathematics and engineering. In most scientific modeling projects, investigators have to deal with very large systems of linear and nonlinear equations. Understanding of which requires powerful computers and a firm understanding of the vast number of existing pertinent algorithms. The main goal of the course is to provide an instruction to algorithmic and mathematical foundations of high-performance scientific computations. Introductory topics of the course include root finding, fixed point methods, interpolation methods, initial value problems and optimization. Particular emphasis will be on optimization methods, including steepest descent, line search methods, newton methods, quasi-Newton methods, trust regions, theory of constraint optimization and linear programming. More Info

**Offered in:**#### MATH 426 Numerical Linear Algebra +

**Description:**

This course is a continuation of linear algebra, towards topics relevant to applications as well as theoretical concepts. Topics to be discussed are algebraic systems, the singular value decomposition (SVD) of a matrix and some of its modern applications. We will discuss Principal Component Analysis (PCA) and its applications to data analysis. We will study linear transformations and change of basis. We will discuss complex vector spaces and Jordan canonical form of Matrices. We will discuss non-negative matrices and Perron-Frobenius Theory. We will explain multiple matrix factorisations, such as LU, QR, NMF. Finally we will discuss other applications such as the Fast Discrete Fourier Transform. For each of these topics we will discuss numerical computer algorithms and their implementations. In particular we will discuss in detail eigenvalue estimation, including iterative and direct methods, such as Hausholder methods, tri-diagonalzation, power methods, and power method with shifts. We will explain concepts of numerical analysis that are important to consider when we talk about the implementation of algorithms, such as stability and convergence. We will discuss iterative methods as well as direct ones, their advantages and disadvantages. The methods are their applications will be illustrated using a common programming language such as python and/or R. More Info

**Offered in:**#### MATH 440 General Topology +

**Description:**

This course is an introduction to the abstract theory of continuity and convergence, otherwise known as general (or point-set) topology. Topics include metric spaces and topological spaces, continuity, subspaces, product and quotient spaces, sequences, nets and filters, separation and countability, compactness, connectedness, and the fundamental group. More Info

**Offered in:**#### MATH 447 Probability Models +

**Description:**

This is an undergraduate course on probability models with a strong emphasis on stochastic processes. The aim is to enable students to approach realworld phenomena probabilistically and build effective models. Topics include probability spaces, random variables, conditional probability, Markov chains, Poisson processes, Brownian motion, probabilistic simulations. More Info

**Offered in:**#### MATH 448 Computational Statistics +

**Description:**

This course is an introduction to the fundamental ideas and techniques of statistical inference. The course demonstrates how and when to use statistical methods, explains the mathematical background behind them and illustrates them with case studies. Topics covered include the Central Limit Theorem, parameter estimation, confidence intervals, hypothesis testing, type I and II errors, power, significance level, p-value, likelihood ration tests, t-test, paired and 2-population t-tests, goodness-of-fit tests, chi-square tests, contingency tables, exact tests, nonparametric tests, ANOVA and regression models. Statistical software such as R, Matlab, or Python, will be used to analyze real-world data. More Info

**Offered in:**#### MATH 450 An Introduction to Real Analysis +

**Description:**

A rigorous treatment of the calculus of functions of one real variable. Emphasis is on proofs. Includes discussion of topology of real line, limits, continuity, differentiation, integration and series. More Info

**Offered in:**#### MATH 455 An Introduction to Statistical Machine Learning +

**Description:**

This course will provide an introduction to methods in statistical machine learning that are commonly used to extract important patterns and information from data. Topics include: supervised and unsupervised learning algorithms such as generalized linear models for regression and classification, support vector machines, random forests, k-means clustering, principal component analysis, and the basics of neural networks. Model selection, cross-validation, regularization, and statistical model assessment will also be discussed. The topics and their applications will be illustrated using the statistical programming language R in a practical, example/project oriented manner. More Info

**Offered in:**#### MATH 458 Theory of Numbers +

**Description:**

This course is an introduction to elementary theory of numbers. Topics include, but are not limited to: divisibility and prime numbers, Euclidean algorithm and applications, congruence arithmetic, primitive roots, quadratic residues, continued fractions, Diophantine linear and quadratic equations, approximations by rationals. More Info

**Offered in:**#### MATH 460 Survey of Geometry +

#### MATH 470 Mathematical Logic +

**Description:**

Syntax and semantics of propositional and first order predicate logic. Axiomatic theories and completeness. Brief discussion of incompleteness results. More Info

**Offered in:**#### MATH 478 Independent Study +

**Description:**

Work done by a student or group of students under faculty supervision on material not currently offered in a regularly scheduled course. Students wishing to undertake such work must first find a faculty member willing to supervise it; the work to be completed must be approved by the department chair. More Info

**Offered in:**#### MATH 480 Special Topics +

**Description:**

An advanced course offering intensive study of selected topics in mathematics. A course offered as MATH 480 is an advanced undergraduate mathematics course being given for the first time and covering topics not available in current courses. Such a course is offered either to fulfill a one-time need or to try out material with the intention of developing a new course. Course content varies each semester and will be announced prior to registration. More Info

**Offered in:**- TBA

#### MATH 490 Thesis Research +

**Description:**

An opportunity for qualified, advanced students wot work on a specialized research project under the guidance of a faculty advisor. More Info

**Offered in:**