UGRD > MATH

## Mathematics

#### 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. Note: Students intending to take Calculus I and II (MATH 140 and 141) should take MATH 130 instead of MATH 129. Students may take MATH 130 after MATH 129, but only with the explicit permission of the department, and then only for two credits. 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. Note: No student will receive graduation credits for MATH 130 if it is taken after successful completion of any higher math course. Students who have successfully completed MATH 130 may not subsequently take MATH 129 for credit. Students may take MATH 130 after MATH 129 only with explicit permission of the department, and then only for two credits. More Info

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

#### 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. Students may not receive graduation credit for both MATH 134 and MATH 135. Students may take MATH 140 after MATH 134, but only with the explicit permission of the department and then only for two credits. 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. Note: No student will receive graduation credit for MATH 135 if it is taken after successful completion of MATH 134 or 140 or a higher Math course.Students may take MATH 140 after 135 only with explicit permission of the Department, and then only for two credits. More Info

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

#### MATH 140 Calculus I +

**Description:**

The first in the sequence of calculus courses for science and math majors. Starts with the basic concepts of functions and limits. Topics covered include: derivatives and their applications, definite and indefinite integrals with applications to geometric and physical problems, and discussion of algebraic and transcendental functions. Note: Math 134 or Math 135 does NOT satisfy the pre-requisites for Math 140. Therefore students who complete Math 134 or 135 will have to take and pass the math placement test to get into Calculus I.Additionally, students who have received credit for either MATH 134 or MATH 135 may not take MATH 140 for credit without the explicit permission of the department and then only for two credits. More Info

**Offered in:**#### MATH 140R Calc I-Reduced Credt +

#### 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 for Reduced Credit +

**Description:**

The course is exactly the same as Math 141 with the exception as to the number of credits that a student will earn for completing this course. Completion of Math 141R will result in 2 credits being earned by the student. Please note that because Math 141R is the second of a sequence of calculus course, it should be taken as soon as possible after Math 140, Math 140R, Math 145 or Math 145R. A student who has received credit for Math 141 or Math 141R may not take Math 146 without permission of the department and then only for two credits as Math 146R. Similarly, a student who has received credit for Math 146 or Math 146R may not take Math 141 without permission of the department and then only for two credits as Math 141R. Students may not earn credit for both Math 141 and Math 141R. 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. Note: Math 134 or Math 135 does NOT satisfy the pre-requisites for Math 145. Therefore students who complete Math 134 or 135 will have to take and pass the math placement test to get into Calculus I. Additionally, students who have received credit for either MATH 134 or MATH 135 may not take MATH 145 for credit without the explicit permission of the department and then only for two credits. Students who complete this course will be eligible for MATH 141, or MATH 146, as well as MATH 303. More Info

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

**Description:**

The course is exactly the same as Math 145 with the exception as to the number of credits that a student will earn for completing this course. Completion of Math 145R will result in 2 credits being earned by the student. Students who complete this course will be eligible for Calculus II (MATH 141), or Calculus II for the Life and Environmental Sciences (MATH 146), as well as Mathematical Biology (Math 303) and any other course in the mathematics department that currently has MATH 140 as a prerequisite. A student who has received credit for either MATH 134, MATH 135 or MATH 140 may take MATH 145R for two credits with the explicit permission of the department.Students cannot earn credit for both MATH 145 and MATH 145R. More Info

**Offered in:**#### MATH 146 Calculus II for Life & Environmental Sciences +

**Description:**

This calculus course presents advanced topics of calculus in the context of the life and environmental sciences. This course does not fulfill the Calculus II (Math 141) requirement and does not serve as a prerequisite for Multivariable Calculus (Math 240). More Info

**Offered in:**- TBA

#### 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. Please note: Because MATH 240 is the third part of the calculus sequence, it should be taken as soon as possible after MATH 141. Note: No student receives graduation credit for MATH 240 if it is taken after successfully completion of MATH 242. Students may take MATH 242 after MATH 240 only with explicit permission of the Department, and then only for one credit. 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. Students who have credit for Math 242 are not allowed to enroll in Math 242R More Info

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

**Description:**

Elementary theory of vector spaces. Topics include linear independence, bases, dimension, linear maps and matrices, determinants, orthogonality, eigenvalues and eigenvectors. 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:**- TBA

#### 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 280 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 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:**- TBA

#### MATH 303 Introduction to Mathematical Biology +

**Description:**

Mathematical models of population growth and other biological processes. Use of math order linear difference equations will be used to model propagation of annuals plants; growth of segmental organisms; red blood cell production; and population growth and destiny dependence in single-species populations. Continuous models will be constructed from among several possibilities, including the logistic equation, simple exponential growth, the Chemostat, Michaelis-Menten kinetics, drug delivery, glucose-insulin kinematics, Gompertz growth in tumors, and the Fitzhugh-Magumo model for neural impulses. Appropriate software will be used throughout the course. More Info

**Offered in:**#### MATH 310 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 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.Students may not receive credit for both MATH 320 and CS 220.Students may not take MATH 320 to receive a better grade in previously taken CS/MATH 320L. More Info

**Offered in:**#### MATH 345 Probability and Statistics I +

**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, Bemoulli, 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 346 Probability and Statistics II +

**Description:**

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: 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. Software suitable for statistical analysis, e.g. R or Matlab, will be used to analyze real-world data. 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 356 Differential Geometry of Curves and Surfaces +

**Description:**

Differential geometry of curves and surfaces in Euclidean spaces, as an introduction to the geometry of Riemannian manifolds. The course presents intrinsic and extrinsic properties, both from a local and global point of view. Topics include; plane and space curves, surfaces, metrics on surfaces, Gaussian curvature, surfaces of constant curvature, shape operator, mean curvature and minimal surfaces, vector fields on surfaces. 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. (Course is offered in the spring only.) 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. (This course is offered as demand requires.) 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:**#### MATH 384L Game Theory, Evolution and Ecology +

**Description:**

Fundamental concepts of evolutionary game theory and their application in biology. Topics include: the strategy and payoff matrix, the game tree, strategic and extensive form games, symmetric games, Nash equilibria. Evolutionary game theory concepts are discussed for two-strategy games (Prisoner's Dilemma, Hawk-Dove) and three-strategy games (Rock-Scissors-Paper). Biological examples are studied, such as blood sharing in vampire bats, competition in bacteria, or the evolution of altruistic punishment.BIOL 384L and MATH 384L are the same course. 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 420 Introduction to Combinatorics +

**Description:**

This course is an introduction to combinatorics: a branch of mathematics that studies the existence, enumeration, analysis, and optimization of discrete structures that satisfy certain properties. Topics include counting distributions and colorings, sieve methods (such as inclusion-exclusion, for example), generating functions, partially ordered sets, and Ramsey theory. Additional topics may be included, such as permutation spaces, matching theory, and elementary graph theory. More Info

**Offered in:**- TBA

#### MATH 425 Numerical Analysis +

**Description:**

Approximations of roots. Finite differences. Interpolation. Numerical solutions of differential and algebraic equations. (This course is offered as demand requires.) More Info

**Offered in:**#### MATH 426 Advanced Linear Algebra, Applications and Numerical Methods +

**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:**- TBA

#### MATH 447 Probability Models +

**Description:**

This is an introductory course on probability models with a strong emphasis on stochastic processes. The aim is to enable students to approach real-world phenomena probabilistically and build effective models. The course emphasizes models and their applications over the rigorous theoretical framework behind them, yet critical theory that is important for understanding the material is also covered. Topics include: discrete Markov chains, continuous-time Markov chains, Poisson processes, renewal theory, Brownian motion and martingales. Optional topics: queuing theory, reliability theory, and random sampling techniques. Applications to biology, physics, computer science, economics, and engineering will be presented. More Info

**Offered in:**- TBA

#### MATH 448 An Introduction to Statistical Learning +

**Description:**

This course will provide an introduction to methods in statistical learning that are commonly used to extract important pattern and information from data. Topics include, linear methods for regression and classification, regularization, kernel smoothing methods, statistical model assessment and selection, and support vector machines. Unsupervised learning techniques such as principal component analysis and generalized principal component analysis will also be discussed. The topics and their applications will be illustrated using the statistical programing language R. More Info

**Offered in:**- TBA

#### MATH 449 Computational Molecular Biology +

**Description:**

Mathematical Biology is a multidisciplinary field of research, primarily focused on the development of mathematical models and computational algorithms to study biological phenomena. While the field is broadly defined, and can encompass several branches of biological and social sciences, the focus in this course is mainly on the molecular biology of the gene and the fundamental of mathematical models relating to the bioinformatics of analyzing high-throughput biological datasets. We will study mathematical models and computational algorithms that are typically used for analysis and interpretation of omic -scale biological datasets, in particular, gene expression data. The topics that will be covered during the course include basics of the sequence alignment algorithms; quantification of gene expression data from microarray and RNA-seq; regression, clustering, and classification models for genetic stratification; response prediction and biomarker discovery, biophysical models of transcriptional gene regulation; post-transcriptional gene regulation by MicroRNAs; structural bioinformatics, and application of Hidden Markov Models (HMMs to the functional annotation of the genome. More Info

**Offered in:**- TBA

#### 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. (Course offered in the spring only.) More Info

**Offered in:**#### MATH 454 Analysis on Manifolds +

**Description:**

This course is an introduction to the framework for modern advanced analysis. Topics include differentiable maps between Euclidean spaces, Implicit and Inverse Function Theorems, manifolds, differential forms, differentiation and integration on manifolds. More Info

**Offered in:**- TBA

#### MATH 458 Theory of Numbers +

**Description:**

Prime numbers; congruences and residues; approximation of real numbers by rationals; diophantine equations. More Info

**Offered in:**- TBA

#### MATH 460 Survey of Geometry +

**Description:**

Topics taken from classical Euclidean geometry and the non Euclidean geometries; projective geometry; lattices; finite geometries. (This course is normally offered at least once every three semesters.) More Info

**Offered in:**#### 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:**#### 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:**