Undergraduate Courses in Mathematics

MTH U010 Algebra Review

Designed for Arts and Sciences, Criminal Justice, and other majors who need to build their algebraic skills in order to succeed in the next math or math-related courses required by their major. Most students will be directed to this course as a result of placement tests.  The concepts covered are: solving first and second-degree equations, slopes and graphs of lines, solving simultaneous equations in several variables, solving rational equations, and graphing inequalities. Threaded throughout the course will be the analysis and solution of "word" problems.  (Does not count toward graduation credit.)

MTH U100 Introduction to College - 1 Credit

A fun course if there ever was one. 

MTH U110 College Algebra

Laws of exponents, roots, graphing of equations and inequalities, special curves (e.g. conic sections), functions and operations on functions, complex numbers, matrices and vectors. If time permits, elementary discrete probability and least-squares curve-fitting.  (Primarily for BSET majors)

MTH U114 Algebra Review & Applications of Algebra

If you think you need this course please see an advisor. 

MTH U115 Applications of Algebra

Covers linear equations and inequalities, systems of equations, matrices and linear programming (geometric and simplex methods), Markov chains, set and set operations, tree diagrams, combinations and permutations, elementary probability and statistics.  (Core category I) 

MTH U117 Interactive Mathematics

Develops problem-solving skills while simultaneously teaching mathematics concepts; particularly suited to students who work well in collaborative groups and who enjoy writing about the concepts they are learning. Assessment is based on tests, portfolios, written projects and solutions to "problems of the week."  Each unit centers around a particular applied problem, which serves to introduce the relevent mathematical topics. These include: linear programming, curve fitting, elements of probability and statistics, and polling theory. (Core category I) 

MTH U120 Algebra Review & Pre-Calculus

If you think you need this course please see an advisor. 

MTH U121 Pre-Calculus

Focuses on linear, polynomial, exponential, logarithmic and trigonometric functions. Emphasis will be placed on understanding, manipulating and graphing these basic functions, their inverses and compositions and using them to model real-world situations (e.g. exponential growth and decay, periodic phenomena).  Equations involving these functions will be solved using appropriate techniques. Special consideration will be given to choosing reasonable functions to fit numerical data. (Does not satisfy core category I)

MTH U130 College Mathematics for Business and Economics

Introduces students to some of the important mathematical concepts and tools (e.g. modeling revenue, cost and profit with functions) used to solve problems in business and economics. The course assumes familiarity with basic properties of of linear, polynomial, exponential and logarithmic functions. Topics include: the method of least squares, regression curves, solving equations involving functions, compound interest, amortization and other consumer finance models.  (Graphing calculator required - see instructor for Make and Model)  (Does not satisfy core category I)

MTH U131 Calculus for Business and Economics

Introduction to differential calculus includes derivatives of power, exponential, logarithmic, logistic functions, and functions built from these. Derivatives are used to model rates of change, to estimate change, to optimize functions, and in marginal analysis. The integral calculus is applied to accumulation functions and future value. The emphasis of the course is on realistic business and economics problems, the development of mathematical models from raw business data, and the translation of mathematical results into verbal expression appropriate for the business setting.  The course also features a term-long marketing project in which students gather their own raw data, model it, and use calculus to make business decisions; each student is responsible for a 10 minute presentation. (Graphing calculator required - see instructor for Make and Model) (Core category I) 

MTH U141 Calclus I

Serves as both the first half of a two semester calculus sequence and as a self-contained one semester coure in differential and integral calculus. Basic concepts and techniques of differentiation and integration are introduced and applied to polynomial, exponential, log and trigonometric functions. The derivative as rate of change and integral as accumulator are emphasized. Applications include optimization, growth and decay, area, volume and motion. 

MTH U142 Calculus II

Continuation of the first semester of basic calculus (MTH141). introduces additional techniques of integration and numerical approximations of integrals; also use of integral tables. Further applications of integrals.  Also, introduction to differential equations and slope fields, and elementary solutions. Introduction to functions of several variables, partial derivatives and multiple integrals.

MTH U151 Calculus & Differential Equations for Biology 1

Begins with the fundamentals of differential calculus and proceeds to the specific type of differential equation problems encountered in biological research.  presents methods for the solutions of these differential equations and how the exact solutions are obtained from actual laboratory data. Topics: Differential Calculus: Basics, The derivative, the rules of differentiation, curve plotting, exponentials and logarithms, trigonometric functions; Using technology to understand derivatives; Biological kinetics:  zero- and first-order processes, processes tending toward equilibrium, bi- and tri- exponential processes,  biological half-life; differential equations: particular and general solutions to homogeneous and non-homogeneous linear equations with constant coefficients, systems of two linear differential equations; compartmental problems: non-zero initial concentration, two compartment series dilution, diffusion between compartments, population dynamics; Introduction to integration.

MTH U152 Calculus & Differential Equations for Biology 2

 Begins with the integral calculus and proceeds quickly to more advanced topics in differential equations. Linear algebra is introduced and matrix methods are used to solve larger systems of differential equations. Advanced topics in reaction kinetics will be covered. The integral and differential calculus of functions of several variables. We then pursue the study of numerical methods in integration and solutions of differential equations. A short introduction to probability follows. Taylor polynomials and infinite series will be covered. Topics: Calculus: definite and indefinite integrals, properties of definite integrals, numerical integration, integration techniques (substitution, parts, partial fractions), improper integrals; Differential Equations: separation of variables, complex roots of characteristic polynomials, nonhomogeneous differential equations with trigonometric right hand side; Linear Algebra: matrices, inverses of matrices, determinants, eigenvalues, matrices and differential equations; Reaction Kinetics: Michaelis-Menten processes,  tracer experiments, inflow and outflow through membranes; Functions of Several Variables: partial derivatives, extrema of functions of several variables, Lagrange multipliers, total differentials, the method of least squares, double integrals; Probability: Discrete random variables, continuous random variables, expected value, variance, exponential random variables, normal random variables; Infinite series and Taylor polynomials: Taylor polynomials, infinite series, series with positive terms, ratio test, Taylor series, probabilities and infinitely many outcomes; Numerical Methods: Riemann sums, numerical solutions of  differential equations, Newton's method. 

MTH U160 Linear Programming

Covers linear equations and inequalities, systems of linear equations, Gauss-Jordan elimination, graphical solution to linear programming problems, algebraic solution by the Simplex method, the principle of duality; applications to optimization and game theory. 

MTH U165 Intro to Mathematical Reasoning

MTH U170 Math Discovery and Computers

Provides students with marketable scientific computing skills, and uses those skills to explore open-ended mathematical problems. Through guided processes of computing, reflecting, discussing, and writing, offers students the opportunity to expand their capacities to think productively about problems that are new to them. Such capacities are useful in all future courses and forms of employment.  

MTH U180 Statistical Thinking

Introduces the way of of statistical thinking to students without using any sophisticated mathematics. The class use extensive class discussion and homework problems to teach students statistical reasoning and to critically evaluate the usage of statistics by others. Readings from a wide variety of sources will be assigned. The topics include descriptive statistics, sampling theory, and fundamentals of statistical inference (confidence intervals and hypothesis testing).  (Core Category II <-- old) 

MTH U201 History of Mathematics

To be filled out later. (Core category II <-- old)

MTH U203 Foundations of Mathematics

Investigates the modern revolutions in mathematics initiated by Cantor, Godel, Turing and Robinson in the fields of set theory, provability, computability and analysis respectively, as well as background on the controversy over the philosophy and underlying logic of mathematics.  (Core category V <- old) 

MTH U230 Probility & Discrete Mathematics

Provides the discrete portion of the mathematical background needed by students in Electrical and Computer Engineering.  Topics include Boolean algebra and set theory, logic, logic gates; growth of functions, algorithms and their complexity; proofs and mathematical induction; graphs, trees, and their algorithms.  As time permits, additional topics may include methods of enumeration and finite state machines. 

MTH U240 Intensive Calclus (Engineering)

Contains the material from the first semester of the engineering calculus sequence (MTH U123), preceded by material emphasizing the strengthening of pre-calculus skills. Topics include: properties of exponential, logarithmic and trigonometric functions, differential calculus, introductory integral calculus. 

MTH U241 Calculus I (Engineering/Science/Math)

Introduces differential calculus and integral calculus, with vectors. Topics covered include: functions, rates of change, velocity and acceleration, tangent lines, rules for differentiation, exponential, logarithmic, trigonometric, and inverse-trigonometric functions, linear approximation, Newton's method, optimization, applications to physics, areas and Riemann sums, displacement, mass, the definite integral, properties of integrals, the fundamental theorem of calculus, integration by substitution, parametric curves, position and velocity vectors, dot product, linear combinations, and lines and planes in three dimensions.

MTH U242 Calculus II (Engineering/Science/Math)

Continues topics on integration from U123, including integration by parts and tables, numerical approximation techniques, improper integrals, and applications of integration to volumes, arclength, work and line integration. Covers simple first- and second-order differential equations, via analytic, numerical, and graphical techniques. Contains applications of differential equations to growth and decay, populations, velocity and acceleration, Newton's Law of Cooling, vibrations, and circuits. Covers infinite series, convergence tests, Taylor series, complex numbers and Euler's formula.

MTH U243 Calculus II (Engineering Technology)

To be filled out later. 

MTH U280 Statistics and Software

Provides an introduction to basic statistical techniques and the reasoning behind each statistical procedures. Students will learn to choose appropriate statistical data analysis methods for applications in health and social sciences. Also teaches using a statistical package such as SPSS or SAS to implement the data analysis on computer. Topics covered include descriptive statistics, elementary probability theory, parameter estimation, confidence intervals, hypothethis testing, nonparametric inference, analysis of variance and regression with a minimum of mathematical derivations.  Prereq: nonmath majors. 

MTH U285 Probility with Statistics

Presents an introduction to probability and probabilistic reasoning, sample spaces, events, and axioms. Studies conditional probability and Bayes' Law, independence, random variables and their distributions, distributions, expected value, and variance. Covers the Law of Large Numbers, and the Central Limit Theorem. Introduces Statistical Inference: confidence intervals, hypothesis testing with levels of significance, and Bayesian Statistics. 

MTH U300 Co-op Reflection Seminar I (1 credit)

Intended for Math majors who have completed their first co-op assignment. Its goal is to examine the mathematical problems encountered on the job, and relate them to courses already taken and to the studentís future program. It is expected that faculty members and other guests will also contribute to the discussion. Grades will be determined by the studentís participation. 

MTH U341 Calculus III (Eng/Sci)

This is the third semester of a calculus sequence for science and engineering students. Linear functions and their matrices are introduced, the derivative is defined as a linear function (Jacobian), and the general chain rule is expressed in matrix form. Topics covered include partial derivatives and tangent planes, the gradient , divergence and curl, multiple integrals, change of variable in multiple integrals, vector fields and line integrals, and Green's theorem. Students are expected to be familiar the calculus of single-variable functions, vectors and parametric curves. Several computer-lab projects will be assigned, using software (Maple, MatLab) available in university computer labs. 

MTH U343 Differential Equations & Linear Algebra

The is the 4th semester of the calculus sequence for engineering students. It covers differential equations, their applications, and techniques for solving them. Topics include 1st and 2nd  order equations, equilibria, stability, resonance, phase-plane analysis, systems (e.g. predator-prey), chaos, impulses and delta functions.  Related topics from linear algebra include systems of equations, row-reduction, eigenvalues and eigenvectors, symmetric matrices and diagonalization; solution techniques include separation of variables, numerical, and Laplace transform. There will be several problem sets requiring the use of software (Excel spreadsheet and MatLab) available at university computer labs. 

MTH U345 Ordinary Differential Euqations

Studies ordinary differential equations with applications: first-order equations and systems, second-order equations, existence theory, analytic solution techniques, and numerical methods. Eigenvalues and eigenvectors are introduced to study systems of equations. Computer labs are used for visualization and numerical approximations.

MTH U371 Linear Algebra

The first half of the course uses the Gauss-Jordan elimination algorithm to analyze and find bases for subspaces such as the image and kernel of a linear transformation. The next group of topics centers around the geometry of linear transformations: orthogonality, the Gram-Schmidt process, rotation matrices and least squares fit. The final part of the course deals with diagonalization and similarity, ending with the spectral theorem and the singular value decomposition. This course is primarily for math and science majors; applications will be drawn from many technical fields. Computation will be aided by the use of software such as Maple or MatLab, and graphing calculators. 

MTH U400 Co-op Reflection Seminar II (1 credit)

Intended for Math majors who have completed their second co-op assignment. Its goal is to examine the mathematical problems encountered on the job, and relate them to courses already taken and to the studentís future program. It is expected that faculty members and other guests will also contribute to the discussion. Grades will be determined by the studentís participation. 

MTH U430 Number Theory

Introductory course in number theory. The topics include: linear diophantine equations, congrue`nces, design of magic squares, Fermat's little theorem, Euler's Formula, Euler's phi function, computing powers and roots in modular arythmetic, the RSA encryption system, primitive roots and indices, the Law of quadratic reciprocity; also, as time permits: diophantine approximation and Pell's equation, elliptic curves, points on elliptic curves modulo p, elliptic curves and Fermat's last theorem. 

MTH U433 Combinatorics

Introduces techniques of mathematical proofs, including mathematical induction. Explores various techniques for counting such as permutation and combinations, inclusion-exclusion principle, recurrence relations, generating functions,  Polya enumeration, and the mathematical formulations necessary for these techniques, including elementary group theory and equivalence relations. 

MTH U441 Chaotic Dynamical Systems

Presents an experimental study, using simple mathematical models, of chaotic behavior in dynamical systems.  (Such systems are frequently found in science and industry.)  Goals include the development of skills of experiment and inquiry, integration of visual and analytical modes of thought, and appreciation of issues of problem formulation and representation. 

MTH U481 Probality and Statistics

Basic course in probability and mathematical statistics. The first part of the course focuses on probability theory, and covers the following topics: sample space; conditional probability and independence; discrete and continuous probability distributions for one and for several random variables; expectation; variance; special distributions, including binomial, Poisson, and normal distributions; Law of Large Numbers and Central Limit Theorem. The second part of the course introduces basic statistical theory, including: estimation of parameters; confidence intervals; hypothesis testing. 

MTH U525 Applied Analysis Seminar

Demonstrates the applications of mathematics to interesting physical and biological problems. Methods are chosen from ordinary and partial differential equations, calculus of variations, Laplace transform, perturbation theory, special functions, dimensional analysis, asymptotic analysis, and other techniques of applied mathematics. 

MTH U530 Numerical Analysis

In practice, computations are never exact. Therefore, the problem of finding efficient methods to calculate sufficiently accurate answers is of fundamental importance. The emphasis of the course is not on recipes for solving problems, on proving theorems, or on writing computer programs. Rather, the practical concerns of efficiency and accuracy are illustrated by studying the following problems: roots of nonlinear equation,  simultaneous linear equations - direct and iterative methods of solution, eigenvalue problem, interpolation, and curve-fitting. Prereq: Two years of calculus and one course in computer programming.

MTH U532 Numerical Solutions of Differential Equations

Covers numerical problems in interpolation, differentiation, integration, Fourier transforms, and the solving of differential equations. Emphasizes practical methods and techniques. The heart of the course is a study of modern methods for finding numerical solutions of ordinary differential equations, both initial value problems and boundary value problems. Homework and projects will be based on MATLAB. U530 is not  prerequisite. 

MTH U541 Advanced Calculus

Offers a deeper and more generalized look at the ideas and objects of study of calculus. Topics may include the generalized calculus of n-space, the inverse and implicit function theorems, differential forms and general Stokes-type theorems, geometry of curves and surfaces, and special functions. 

MTH U545 Fourier Series and Partial Differential Equations 

Studies boundary value problems for ordinary differential equations, including eigenvalues and eigenfunctions, Fourier series, and applications to partial differential equations, including heat transfer and vibrations. Computer labs are used for visualization and numerical approximation.

MTH U550 Real Analysis 

Provides the theoretical underpinnings of calculus and the  advanced study of functions. Emphasis throughout is on precise definitions and rigorous proof. Topics include the real numbers andand their completeness, continuity and differentiability, the Riemann integral, the Fundamental Theorem of Calculus, inverse function and implicit function theorems, limits and convergence.This course is required of all mathematics majors. 

MTH U555 Complex Variables

Provides an introduction to the analysis of functions of a complex variable.  Starting with the algebra and geometry of complex numbers, basic derivative and contour integral properties are developed for elementary algebraic and transcendental functions as well as for other analytic functions and functions with isolated singularities. Power and Laurent series representations are given. Classical integral theorems, residue theory, and  conformal mapping properties are studied. Applications of harmonic functions are presented as time permits. 

MTH U560 Geometry 

Studies classical geometry and symmetry groups of geometric figures, with an emphasis on euclidean geometry. Teaches how to formulate mathematical propositions precisely and how to construct and understand mathematical proofs.  Provides a line between classical and modern geometry with the aim of preparing students for further study in group theory and differential geometry. 

MTH U565 Topology 

Introduces the student to fundamental notions of topology.  After a brief introduction to basic Set Theory, the course covers the foundations of General Topology (axioms for a topological space, continuous functions, homeomorphisms, metric spaces, the subspace, product, and quotient topologies, connectedness, compactness, the Hausdorff condition).  The rest of the course is an introduction to Algebraic and Geometric Topology (homotopy, covering spaces, fundamental groups, graphs, surfaces, manifolds) and applications. Additional topics may be covered if time allows.

MTH U571 Advanced Linear Algebra 

Provides a more detailed study of linear transformations and matrices: LU factorization, QR factorization, Spectral Theorem and singular value decomposition, Jordan form, positive definite matrices, quadratic forms, partitioned matrices, norms and numerical issues. Topics and emphasis can change from year to year. 

MTH U575 Group Theory 

Presents basic concepts and techniques of the group theory: symmetry groups, axiomatic definition of groups, important classes of groups (abelian, cyclic, additive and multiplicative groups of residues, permutation groups), Cayley table, subgroups, group homomorphisms, cosets, the Lagrange theorem, normal subgroups, quotient groups, direct products. Studies structural properties of groups.  Possible applications include geometry, number theory, crystallography, physics, and combinatorics.

MTH U576 Rings and Fields 

Introduces commutative rings, ideals, integral domains, fields and the theory of extension fields. Topics include Gaussian integers, Galois groups, and the fundamental theorem of Galois theory. Applications include the impossibility of angle-trisection and the general insolvability of 5th and higher degree polynomials; other topics as time permits. 

MTH U581 Statistics and Stochastic Processes 

Continuation of MTH U285 (Probability and Statistics).  The first part of the  course covers classical  procedures of statistics including : the t-test, linear regression, and the  chi-square test. The second part provides an introduction to stochastic  processes, with emphasis on Markov chains, random walks and Brownian  motion, with applications to modeling and finance.

MTH U585 Introduction to Actuarial Practice 

Basic aspects of life contingencies are introduced. The theory is illustrated by worked examples, and reinforced through numerous exercises. The course prepares students to take the relevant actuarial exam. 

MTH U725 Applied Mathematics Capstone 

Offers students of mathematics the experience of utilizing their skills to study problems that arise in industry and other "real world" settings. Students will have the opportunity to build on exciting industrial experiences they may have had through co-op or other employment.  This seminar satisfies the Arts and Sciences experiential education requirement, and is intended for juniors and seniors with some experience or interest in applications of mathematics. 

MTH U790 Acturarial Practice

Prepares students for the first actuarial exam by covering omitted from MTH U387, and by practice with actual exam questions. Introduces utility and risk theory. Students must submit a major project analyzing data from their co-op experience or from current actuarial, financial , or health-care policy literature.

MTH U921-924 Generic Directed Study (921=1 credit; 922=2 credits; 923=3 credits; 924=4 credits)

Offers independent work on chosen topics under the direction of members of the department. 

MTH U951 Experential Education Directed Study 

This individualized course draws upon the student's approved experiential activity and integrates it with study in the academic major. It is restricted to those junior and senior mathematics majors who are using it to fulfill their experiential education requirement; for these students it may count as a mathematics elective, subject to approval by instructor and advisor.

MTH1000 Mathematics Preliminaries 1

Supplies, together with MTH1010, the high school math background necessary for a student to enroll in MTH1101 ,MTH1106 , or MTH1113. Includes the arithmetic of signed numbers, fractions, decimals, and percents; operations on polynomials; solving simple first degree equations; and laws of exponents. Prereq: Permission of course coordinator. [More Information]

MTH1010 Mathematics Preliminaries 2

Supplies, together with MTH1000, the high school background necessary for a student to enroll in MTH1101, MTH1106, or MTH1113. Includes solving first and second degree equations and systems of equations; graphic lines and parabolas; solving equations with algebraic fractions; solving word problem applications. Prereq: Permission of course coordinator. [More Information]

MTH1101 Applications of Algebra

Examines linear equations and their graphs, and systems of linear equations and linear inequalities in two variables, with application to linear programming. Introduces matrices with application to Markov chains; set theory, techniques of counting; permutations and combinations and elementary probability. (Core Category I) 

MTH 1102 Interactive Mathematics

Designed for students who enjopy working in collaborative groups. Hands-on explorations of real-life situations, developing concepts from algebra, statistics, and linear programming as needed. Problem solving strategies emphasized. (Core Category I) A graphing calculator is required for this course; the TI-83 is strongly recommended. [Home Page]

MTH1106 Functions and Algebra

Examines how to solve various kinds of algebraic equations: linear, quadratic, and linear systems in two and three unknowns. Considers applications to word problems such as motion, mixture, and variational problems. Covers the concept of function, graphs, line slopes, and graphs of polynomials. Also discusses some elementary trigonometry and vectors in the plane. Students do not receive credit for this course if they have already received credit for MTH1188 or MTH1191. [More Information]

MTH1107 Functions and Basic Calculus

Introduces differential calculus. Examines elementary rules of differentiation with application to graph sketching and to maximum and minimum problems. Discusses exponential and logarithmic functions with application to compound interest, population growth, and radioactive decay. (Core Category I) Prereq. MTH1106. Students do not receive credit for MTH1107 if they already received credit for MTH1114 . [More Information]

MTH1108 Basic Calculus 2

Offers a review and continuation of differential calculus, graphing and differentiation of trigonometric functions; also presents an introduction to integral calculus with applications to geometric problems and differential equations. 

MTH1113 College Mathematics for Business and Economics

Focuses on the analytic, geometric, and numerical properties of linear, exponential, logarithmic, polynomial, and logistic functions. These functions are studied in the context of using them to model a variety of situations in economics and business including simple and compound interest; mortgages, and the present and future value of both one-time payments and multiple payments/withdrawals. A graphing calculator is required for this course. [More Information]

MTH1114 Calculus for Business and Economics

Studies functions, derivatives, differential of polynomials, exponential functions and logarithmic functions; graphics functions using maximum, minimum, inflection points; and optimization in nonlinear problems; marginal analysis of cost, revenue, profit functions. Emphasizes work problems and applications. A graphing calculator is required for this course; the TI-83 is strongly recommended. Prereq: MTH1113 or equivalent. Students do not receive credit for MTH1114 if they have already received credit for MTH1107. [More Information]

MTH1120, MTH1121 Intensive Calculus 1 and 2

Assists students in overcoming deficiencies in pre calculus mathematics without loosing ground in the MTH1123 sequence. Reviews high school algebra, introduces trigonometric functions, and covers the material in MTH1123 and MTH1124. Includes lecture and homework review sessions. (Students are placed in this course by request, or on the basis of their College Board scores and the result of an orientation-week diagnostic test.) 

MTH1123 Calculus for Engineering Majors 1

Introduces the differential calculus of one variable, including trigonometric, exponential, and logarithmic functions, together with their graphs. Includes average rates of change, instantaneous rates of change, derivatives and the chain rule. Covers curve sketching, applications of the derivative to problems involving related rates, and maxima and minima. [More Information]

MTH1124 Calculus for Engineering Majors 2

Introduces integral calculus including areas, volumes, and other applications. Studies integration involving trigonometric, inverse trigonometric , exponential, and logarithmic functions. Prereq: MTH1123.[More Information]

MTH1125 Calculus for Engineering Majors 3

Introduces Taylor polynomials and series; studies differential equations and mathematical models. Prereq: MTH1124.[More Information]

MTH1133 Calculus for Biology Majors 1

Begins with the fundamentals of differential calculus and proceeds to specific problems encountered in biological research. Studies the formulation of psychological problems in terms of differential equations; solutions of differential equations by method of undetermined coefficients; and application to compartmental problems. 

MTH1134 Calculus for Biology Majors 2

Studies integral calculus; trigonometric functions; solutions of differential equations by separation of variables; and advanced compartmental problems. Introduces pharmaco-kinetics, numerical integration, and Euler's method. Prereq: MTH1133.

MTH1135 Calculus for Biology Majors 3

Presents functions of several variables, Taylor polynomials, and infinite series. Prereq: MTH1134.

MTH1137 Discrete Mathematics 1

Covers logic, binary arithmetic, basic set theory, Boolean algebra, and logic gates and their close interconnections. Also studies functions, permutations, combinatorics, proof by induction, algorithms, recursion, and recurrence relations. Prereq: MTH1123.[More Information]

MTH1139 Modeling with Functions

Reviews Algebra, Geometry and Trigonometry from a precalculus perspective. Examines linear, polynomial, rational, trignometric, exponential/logarithmic functions, their mathematical behavior, and their use in modeling real-world phenomena. Emphasis on developing strong algebraic skills and understanding. This course is primarily for computer science students. 

MTH1140 Calculus for Science Majors 1

The sequence MTH 1140-2 is equivalent to MTH 1123-5, but geared towards majors in mathematics, physics, chemistry, and computer science. MTH 1140 introduces differential calculus of one variable, including trigonometric, exponential, and logarithmic functions, together with their graphs. Includes average and instantaneous rates of change, derivatives, and the chain rule. Covers applications of the derivative to curve sketching, related rates, and optimization. 

MTH1141 Calculus for Science Majors 2

Introduces integral calculus including areas, volumes, and other applications. Studies integration involving trigonometric, inverse trigonometric, exponential, and logarithmic functions. Prereq: MTH1140.

MTH1142 Calculus for Science Majors 3

Introduces Taylor polynomials and series; studies differential equations and mathematical models. Prereq: MTH1141.

MTH1150 Probability, Statistics and Computer

Presents a computer-oriented introduction to statistical methods, with applications to social and life sciences. Examines descriptive statistics, elementary probability, correlation, and regression, and the fundamentals of statistical inference (confidence intervals and hypothethis testing) with a minimum of mathematical derivations. Uses a statistical computer package such as MINITAB or SPSS to solve supplementary problems. Prereq: nonmath majors.

MTH1152 Statistical Thinking

Introduces the statistical style of thinking for students without mathematical sophistication or who ordinarily do not like mathematics. Assigns readings from a wide variety of sources. Uses extensive class discussion and homework problems to teach students to use statistics and to critically evaluate the use of statistics by others. Covers descriptive statistics, statistical tests, confidence intervals, regression and sampling. (Core Category II) Economics majors do not receive credit for this course if they have alrea dy earned credit for ECN1250 or MSC1201.

MTH1170 Mathematical Discovery and Computers

Introduces the computer as a tool for mathematical discovery as well as an object of study. Both the mathematical and computer components may vary, but there will always be an emphasis on the nature of mathematical exploration and the solving of challenging problems. 

MTH1187 Probability

Presents an introduction to probability and probabilistic reasoning, sample spaces, events, and axioms. Studies conditional probability and Bayes' Law, independence, random variables and their distributions, joint distributions, expected value, and variance. Topics also include the law of large numbers, central limit theorem, and the use of probability in statistical inference. Prereq: MTH 1137 or equivalent.

MTH1188 Problem Solving and Pre-Calculus 1

Develops basic algebraic and problem-solving skills in students who these needs and are enrolled in this course rather than the four-credit MTH1191. Together with MTH1189, prepares the student for calculus (MTH1193). Includes writing equations and relating word problems to equations, plotting linear equations, word problems involving algebraic fractions, algebraic operations, radicals, inequalities, functional notation and the graphing of functi ons. A graphing calculator is required for this course; the TI-85 or 86 is strongly recommended. Students who earn credit for this course may not receive credit for this course may not receive credit for MTH1106 or MTH1191.

MTH1189 Problem Solving and Pre-Calculus 2

Continues MTH1188. Includes functions and graphing, composite functions and inverse functions, logarithmic and exponential functions and equations, trigonometric functions and their graphs, solving trigonometric problems, trigonometric identities, and vectors in two dimensions.

A graphing calculator is required for this course; the TI-85 or 86 is strongly recommended.

Equivalent to MTH1192. 

MTH1191 College Algebra

Examines laws of exponents, factoring, operations with fractional expressions, radical and complex numbers, Pythagorean Theorem and distance formula, linear and quadratic equations and inequalities, and functional notation. Includes graphing of a wide variety of functions and equations, including lines, conic sections, and polynomials. Studies solutions to many types of equations, including linear, quadratic, and polynomial. Also explores many applications of algebra. A graphing calculator is required; either the TI-83 or TI-86 is recommended. Prereq: BSET majors only. Students who earn credit for this course may not receive credit for MTH1106 or MTH1188.

MTH1192 Pre-Calculus 

Studies exponential and logarithmic functions, trigonometric functions of angles in degrees and radians, trigonometric identities and equations, right triangles, law of sines and cosines, inverse trigonometric functions, and polar coordinates. Examines complex numbers in trigonometric form, systems of linear and nonlinear equations, binomial theorem, arithmetic and geometric sequences and series. A graphing calculator is required; either the TI-83 or TI-86 is recommended. Equivalent to MTH1189. Prereq: MTH1191;BSET majors only.

MTH1193 Calculus 1 

Studies general function operations, theory and evaluation of limits, derivatives of algebraic and trigonometric functions, general rules of differentiation, Rolle's Theorem and Mean Value Theorem. Also covers applications of differentiation including velocity; and accelerations, related rates, maximum, minimum, curve sketching, and approximations by differentials. A graphing calculator is required; either the TI-83 or TI-86 is recommended. (Not equivalent to MTH1123. Prereq: MTH1192; BSET majors only. 

MTH1194 Calculus 2

Begins with antidifferentiation and the solution of problems solved by simples differential equations. Examines the Riemann sum and the development of the fundamental theorem with applications to areas, volumes, and rectilinear motion problems. Topics include logarithmic, exponential, and inverse trigonometric functions and their applications. Studies techniques of integration including parts, partial fractions, substitution, and the use of tables, L'Hopital's rule, improper integrals, and geometry of vectors in a plane and space. A graphing calculator is required; either the TI-83 or TI-86 is recommended. (Not equivalent to MTH1124). Prereq: MTH1193;BSET majors only.

MTH1195 Calculus 3 

Begins with sketching surfaces in space leading to a study of functions of several variables, partial derivatives, multiple integrals with applications to area and volume. Studies sequences and series to the development of Taylor and Maclaurin series. Introduces differential equations including the solution, with applications, of first-order variables separable, first-order linear, and second-order linear homogeneous.

A graphing calculator is required; either the TI-83 or TI-86 is recommended.

(Not equivalent to MTH1125).Prereq: MTH1194; BSET majors only.

MTH1203 History of Mathematics 

Traces the development of various branches of mathematics from ancient times to the present, with emphasis on the mathematics itself as well as the mathematicians and cultures that produced it . Teaches students to compute in other number systems, to perf orm geometric constructions, and to learn proofs of some important theorems. (Core Category III) Prereq: interest in history of mathematics.

MTH1212 Linear Programming

Presents an introduction to concepts and techniques of linear programming, game theory, discrete modeling (shortest path, minimum spanning tree). Explores application to economics, social sciences, and other related fields. Prereq: one year of college mathematics.

MTH1223 Calculus for Engineering majors 4 

Covers partial derivatives and multiple integrals, with applications. Prereq: MTH1125 or equivalent.

MTH1225 Differential Equations (Engineering) 1 

Studies ordinary differential equations with applications including mechanical vibrations and electrical circuits. Focuses on first-order equations and systems and second-order linear equations studied from various points of view: existence theory, analytic solution techniques (including Laplace transform), and numerical methods. Uses computer labs for visualization and numerical approximation. Prereq: MTH1125 or equivalent. [More Information]

MTH1226 Differential Equations (Engineering) 2 

Studies partial differential equations with applications. Discusses mathematical models, boundary and initial conditions, Fourier series, and solutions to the wave, diffusion, and Laplace equation. Computer labs are used for visualization and numerical approximation. Prereq: MTH1225 or equivalent. [More Information]

MTH1230 Linear Algebra for Engineers 

Introduces matrices through Gaussian elimination. Proceeds to vector spaces and linear equations; orthogonality; eigenvalues and eigenvectors. Emphasizes engineering applications such as systems of ordinary differential equations. Prereq: MTH1225.[More Information]

MTH1237 Discrete Mathematics 2 

Covers elements of number theory with an application to public key codes, and elements of group theory with an application to error-detecting and error-correcting codes. Prereq: MTH1137.

MTH1238 Combinatorial Mathematics 

Introduces techniques of mathematical proofs, including mathematical induction. Explores various techniques for counting such as permutation and combinations, inclusion-exclusion principle, Polyaenumeration, and the mathematical formulations necessary for these techniques, including elementary group theory and equivalence relations. Prereq: Two courses in calculus.

MTH 1240 Chaos & Fractals 

Presents an experimental study, using simple mathematical models, of chaotic behavior in dynamical systems found in mathematics, science, and computer science. Goals include the development of experimental skills, integration of visual and analytical modes of thought, and an appreciation of issues of problem formulation and representation. Prereq. MTH 1125, MTH 1137, and COM 1201 or equivalent.

MTH1243 Calculus for Science Majors 4

Focuses on methods of calculus and vector analysis to study curves, surfaces, and functions of several variables. Studies parametrization of lines and planes, tangents and normal vectors, partial derivatives, maxima and minima problems, linear approximati on, and tangent planes. Some linear algebra. Prereq: MTH1142 or equivalent. [More Information]

MTH1244 Calculus for Science Majors 5 

Continues MTH1243. Covers multiple integration, line integrals, and exact differentials; various forms of Stoke's theorem; and more linear algebra. Prereq: MTH1243. [More Information]

MTH1245 Differential Equations (Science) 1 

Studies ordinary differential equations with applications . Focuses on first-order equations and systems and second-order linear equations studied from various points of view: existence theory, analytic solution techniques, and numerical methods. Introduces eigenvalues and eigenvectors to study systems of equations. Uses computer labs for visualization and numerical approximation. Prereq: MTH1142 or equivalent. [More Information]

MTH1246 Differential Equations (Science) 2 

Studies partial differential equations with applications. Discusses mathematical models, boundary and initial conditions, Fourier series, and solutions to the wave, diffusion, and Laplace equation. Computer labs are used for visualization and numerical approximation. Prereq: MTH1245 or equivalent.

MTH1290 Mathematics Statistics for Engineers and Scientists with an Introduction to Statistical Software

This course is an introduction to statistics and its scientific and engineering applications, with emphasis on statistical data analysis using well-known software packages SAS and SPSS. Topics include descriptive statistics, computing probability and simple stochastic simulation, parameter estimating, hypothesis testing, correlation and simple regression analysis. Prereq: A calculus course and a probability course such as MTH1187 or MTH1384 or MTH1387. 

MTH1301 Linear Algebra 1 

Focuses on vectors and vector spaces, including function spaces, subspaces. Examines lengths, angels, scalar products; volumes, determinants; linear independence and dependence, dimension, linear and affine maps, kernel and image. Studies algorithms: row operations, double triangular form, inversion. Introduces linear maps. Gives particular attention to characteristic polynomials, eigenvalues, and eigenvectors in low dimensions. Prereq: MTH1244.

MTH1302 Linear Algebra 2 

Focuses on detailed study of linear maps. Studies symmetric maps and quadratic forms, isometries, skew-symmetric maps; decomposition of general linear maps using symmetric maps and isometries. Covers polynomials evaluated on linear maps, generalized eigen spaces, Jordan form. As time permits, introduces computational methods, with emphasis both on geometry underlying algorithms and on particular advantages and limitations. Surveys related areas in mathematics in which linear ideas play a role. Prereq: MTH1301 or equiv.

MTH1311 Real Analysis 1 

Provides a theory and technique for a rigorous treatment of calculus. Topics vary and may include the construction of the real numbers, continuity and convergence, differentiation and integration, and proofs of selected results such as the inverse and imp licit function theorems. Emphasizes careful proofs throughout. Prereq: MTH1238 and MTH1243, or permission of the instructor.

MTH1312 Real Analysis 2

Continues MTH1311. Focuses on calculus, applying the concepts introduced in MTH1311. Prereq: MTH1311.

MTH1321 Introduction to Groups and their Applications

Presents examples of groups (symmetry groups, permutation groups, matrix groups, cyclic groups) and their subgroups. Studies finite groups and orders of subgroups; homomorphisms and normal subgroups. Also considers applications to some of the following, depending on time and interest: geometry, number theory, crystallography, physics, and combinatorics. 

MTH1322 Topics in rings, Fields and Number Theory

Introduces commutative rings, ideals, integral domains, fields, and Galois theory. Studies extension fields, Gaussian integers, and the same topics as time permits. Prereq: MTH1321.

MTH1330 Number Theory

Introduces the elementary methods of analytic number theory. Focuses on divisibility, congruences, arithmetical and multiplicative functions, quadratic reciprocity, and equivalent formulations of the prime number theorem. Prereq: MTH1301, or permission of the instructor.

MTH1337 Foundations of Mathematics 1

Studies the following topics and the shifts in perspective that their development brought about: disputes over the basics for calculus, twentieth-century discoveries in mathematical logic, and the advent of the computer. (Core Category V.) 

MTH1347 Applied Analysis

Demonstrates the application of mathematics to interesting physical and biological problems. Examines methods chosen from ordinary and partial differential equations, calculus of variations, Laplace transforms, singular perturbations, special functions, dimensional analysis, and other techniques of applied mathematics. Prereq: MTH1246, or permission of instructor. [More Information]

MTH1349 Numerical Analysis 1

In practice, computations are never exact. Therefore, the problem of finding efficient methods to calculate sufficiently accurate answers is of fundamental importance. The emphasis of the course is not on recipes for solving problems, proving theorems, or on writing computer programs. Rather, the practical concerns of efficiency and accuracy are illustrated by studying the following problems: roots of nonlinear equation, simultaneous linear equations, interpolation, and curve-fitting. Prereq: Two years of calculus and one course in computer programming.

MTH1350 Discrete Algorithms in Analysis

Analyzes problems in differential equations, integration, and ordinary differential equations. (Does not require prior knowledge of differential equations; MTH1349 is not a prerequisite.) Emphasis is similar to that of MTH1349. Prer eq: Two years of calculus and one course in computer programming.

MTH1351 Functions of a Complex Variable 1

Focuses on algebra and geometry of complex numbers; concepts of limit, continuity, and derivative in the complex domain; homomorphic functions, series, contour integration; and applications. Prereq: MTH1243 or equiv.

MTH1352 Functions of a Complex Variable 2

Continues MTH1351. May include conformal mapping, analytic continuation, Riemann surfaces, the Laplace transform and inverse transform, elliptic functions, and applications. Prereq: MTH1351 .

MTH 1360 Seminar in Applied Mathematics

This course is intended to give students of mathematics the experience of utilizing their skills to study problems that arise in industry and other "real-world" settings. It will also provide the opportunity to build on exciting industrial experiences that they may have had (through Co-op or other employment). Prereq. Junior or Senior status and some experience or interest in applied mathematics. This course satisfies the College of Arts & Sciences Experiential Education requirement for math majors. [More Information]

MTH1367 Geometry 

Studies classical Euclidean geometry and symmetry groups of geometric figures by an analytic approach. Teaches how to formulate mathematical propositions precisely and how to construct and understand mathematical proofs Provides a line between classical and modern geometry with the aim of preparing students for further study in group theory and differential geometry. Prereq: Basic linear algebra or permission of the instructor.

MTH1372 Topology 

Introduces the student to fundamental notions of topology, including: basic set theory, the axioms for a topological space, continuous functions, metric spaces, the subspace, product, and quotient topologies, connectedness, compactness, the Hausdorff condition, surfaces, and the fundamental group. Additional topics may be covered if time allows. 

MTH1384 Probability for Engineering 

Discusses sample spaces; axioms of probability; random variables and their distributions; expectation, moments, and characteristic function; bivariate distributions; jointly Gaussian random variables; stochastic processes, including autocorrelation function and power spectral density; and estimation of the mean and autocorrelation function in the presence of noise. Prereq: MTH1223 and MTH1225 or equiv. [More Information]

MTH1387 Probability 1 

Focuses on probability functions for finite and infinite spaces; conditional probability and independence; discrete and continuous probability distributions for one or more random variables; expectation; moments; binomial, Poisson, and normal distribution s; Law of Large Numbers; and central limit theorem. Prereq: MTH1223 or MTH1244 .

MTH1388 Probability 2 

Studies selected topics, including introduction to stochastic processes, with emphasis on Markov chains or random walk. Prereq: MTH1384 or MTH1387 .

MTH1390 Mathematical Statistics 

Focuses on estimation of parameters, confidence intervals, hypothesis testing, regression, sampling distributions. Prereq: MTH1384 or MTH1387 .

MTH1393 Intro to Actuarial Mathematics 

Basic aspects of life contingencies. The theory is illustrated by worked examples, and reinforced through numerous exercises. The course prepares students for the relevant actuarial exam. 

MTH1395 Actuarial Practice 

Covers topics in statistics and probability omitted from MTH 1387 and 1390, e.g. moment generating funcitons, regression, chi-square tests. Completes preparation for the second actuarial exam. Introduces utility theory and risk theory, Students do a major project analyzing data from their co-op experiences, or current actuarial or health-care policy literature. This course satisfies the College of Arts & Sciences Experiential Education requirement for math majors. 

MTH1714, 1723-5, 1726, 1733-5, 1740-2

Honors Program 

Special sections for honors students of courses MTH1114, MTH1123-5, MTH1223, MTH113-5, MTH1140-2 respectively. 

MTH1801-1808 Directed Study 

Gives highly motivated students the opportunity to explore mathematical situations and theories in depth. Can be used as an opportunity to examine familiar material in fresh ways or to explore new material not offered in formal courses. Provides students strong in mathematics and the related sciences a chance to develop the art and skill needed to work independently and creatively in mathematics. Prereq: Permission of instructor. Students strong in mathematics are permitted to enroll in graduate mathematics courses.

MTH1809 Directed Study: Problem Solving

Emphasizes mathematical problem-solving techniques from a range of areas, including, but not limited to integration, differentiation, number theory, group theory, field theory, combinatorics, linear algebra, differential equations, and mathematical modeli ng. The mathematical model aspect constitutes one third to one half of the course. Analyzes specific realworld models in complete detail, including running and analyzing computer simulations. Requires students to make a number of presentations to the class demonstrating specific techniques. Prereq: Permission of instructor.

MTH1810-1811 Directed Study

Same description as MTH1801-1808; offered for less intensive projects. Prereq: Permission of instructor.

MTH1825-1828 Junior/Senior Honors Project

For details contact the honors office. 

MTH1888-1889 Experiential Education Directed Study 

Draws upon the student's approved experiential activity and integrates it with study in the academic major. Restricted to those students who are using it in fulfilling their experiential education requirement.