Mathematics Degrees

04 Mathematics for Elementary Teachers 1 unit
Spring
Prerequisites: Three years of college-preparatory mathematics (or its equivalent). Priority given to students in the elementary education program.
An investigation of mathematics (arithmetic, geometry, algebra, problem solving) for elementary school teachers. Topics will be chosen from: sets, relations and functions; numeration systems; whole numbers and their operations; number theory; rational numbers and fractions; decimals and real numbers; geometry and measurement; and probability and statistics. The emphases will be on doing mathematics, using manipulatives and developing intuition and problem-solving skills. Laboratory.

109 Statistical Methods 1 unit
Fall, Spring
Prerequisite: Permission of instructor.
Descriptive statistics, probability, sampling distributions, hypothesis testing, parameter estimation, confidence intervals, linear regression, curve fitting, analysis of variance and non-parametric statistics are discussed. The Minitab statistics package is used. Students may not receive credit for both Mathematics 109 and 210. Usually not open to students who have had Mathematics 141.

119 Finite Mathematics for Decision Making 1 unit
Spring
An introduction to discrete mathematics. Applications are drawn from diverse areas including biological sciences, economics, political science and personal finance. Topics in discrete mathematics typically include graph theory, management science, statistics, the mathematics of social choice, game theory, and the logical foundations of mathematics. Interconnections among science, mathematics, and technology with society, environment, and self are central themes. The course is designed for non-majors.

125 Functions 1 unit
Fall, Spring
A modern, unified approach to algebra, trigonometry, logarithms and analytical geometry based on the concept of a function. Linear equations and inequalities, quadratic equations and inequalities, polynomials and rational functions, logarithms and exponential functions, trigonometric and inverse trigonometric functions, and analytic geometry (the circle, the parabola, the ellipse and the hyperbola) will be covered. Emphasis will be given to the use of graphing calculators and on the use of mathematics as a problem-solving tool. Applications in natural science, social science and business will be discussed. This course also serves as a preparation for calculus. Well-prepared students who already have a strong working knowledge of algebra, trigonometry, and logarithms should elect Mathematics 141 in place of Mathematics 125. A graphing calculator is required.

141 Calculus of a Single Variable I 1 unit
Fall, Spring
Prerequisite: Mathematics 125 or equivalent.
Mathematics 141 and 143 constitute a thorough introduction to calculus for students who intend to continue in mathematics and for those who will use calculus in other fields such as science and engineering. Mathematics 141 covers limits, continuity, derivatives and a brief introduction to integration. Applications to problems in related rates, optimization, solid geometry and elementary mechanics are covered. Requires a strong working knowledge of algebra and trigonometry. Students who are weak in these areas should elect Mathematics 125. A graphing calculator is required.

143 Calculus of a Single Variable II 1 unit
Fall, Spring
Prerequisite: Mathematics 141 or equivalent.
Second half of the standard one-year calculus sequence (see Mathematics 141above). Mathematics 143 covers techniques of integration, applications of the integral, simple differential equations with their associated mathematical models, sequences, and series. Requires a strong working knowledge of algebra, trigonometry, derivatives, and some familiarity with integration, including Riemann sums and the Fundamental Theorem of Calculus. Students with a calculus background who are weak in these areas should elect Mathematics 141. A graphing calculator is required.

210 Introduction to Statistical Analysis 1 unit
Fall, Spring
Prerequisite: Mathematics 141 or its equivalent.
Topics include descriptive statistics, principles of probability, random variables, sampling distributions, point and internal estimation, hypothesis testing, analysis of variance, regression and non-parametric statistics. Substantial use is made of Minitab statistics program on the computer. Students may not receive credit for both Mathematics 109 and 210.

236 Linear Algebra 1 unit
Spring
Prerequisite: Mathematics 143, or Mathematics 239, or permission of instructor.
Vector spaces, matrices, Gauss-Jordan reduction, products, dimension, linear transformations, eigenvalues and eigenvectors, and a selection of applications of linear algebra to other disciplines. Throughout this course, students will develop their skills at mathematical writing and their ability to create mathematical proofs. Properties of equality, logical implication, proof by contradiction, quantification and proof by induction will be illustrated in context.

239 Discrete Structures 1 unit
Fall, Spring
Prerequisite: Mathematics 141.
A survey of discrete mathematics with topics selected from set theory, functions and relations, number theory, combinatorics, graph theory, logic (predicate calculus, quantifiers), introduction to proof techniques, and probability.

245 Multivariate Calculus 1 unit
Fall
Prerequisite: Mathematics 143.
Vectors, inner and cross products, and vector-valued functions including parametric representations of curves and surfaces in space. Partial differentiation, the chain rule, function gradients, implicit differentiation, multivariate optimization, and Lagrange multipliers. Multiple integrals and vector analysis, including divergence and curl of vector fields, as well as the theorems of Green, Stokes, and Gauss.

247 Differential Equations & Linear Algebra 1 unit
Spring
Prerequisite: Mathematics 245.
First-order differential equations and numerical algorithms of Euler and Runge-Kutta. Linear algebraic systems, Gaussian elimination, row-echelon form, matrix algebra, inverses and determinants. Vector spaces, subspaces, linear independence, bases, span, dimension, linear mappings, and function spaces. Second and higher-order linear differential equations. Eigenvectors, eigenvalues, and spectral decomposition methods. First order linear differential systems, including solutions methods using matrix exponentials. Applications focus on problems in physics, chemistry, biology, economics and engineering. Time permitting, additional topics include nonlinear dynamical systems, stability theory, transform theory, and power series solutions.

299 Colloquium in Mathematics & Computer Science I 1/4 unit
Fall, Spring
Offered only on a credit/no credit basis.
Prerequisite: Mathematics 143 or Computer Science 173.
Selected topics in mathematics and computer science as presented by students, departmental faculty and visiting speakers. In addition to submitting written summaries of each presentation, students also write a paper on a mathematics/computer science topic of personal interest.

309 Mathematical Statistics 1 unit
Fall
Prerequisite: Mathematics 236 or 245.
A mathematical study of probability distributions, random sampling, and topics selected from statistical theory: estimation, hypothesis testing, and regression.

310 Applied Mathematical Statistics 1 unit
Spring of odd-numbered years
Prerequisite: Mathematics 309.
A continuation of Mathematics 309. In-depth studies of regression analysis, analysis of variance, experimental design, and nonparametric statistics are included. Topics pertinent to actuarial mathematics are also covered.

316 Numerical Analysis 1 unit
Fall of odd-numbered years
Prerequisites: Mathematics 247 or 236, and Computer Science 171.
Methods of obtaining numerical solutions to mathematical problems. The implementation and error analysis of algorithms are stressed. Topics include: solution of non-linear equations, systems of equations, interpolating polynomials, numerical integration and differentiation, numerical solution to ordinary differential equations, and curve fitting.

326 Operations Research 1 unit
Spring of odd-numbered years
Prerequisites: Mathematics 236 or 247, and Mathematics 245.
An introduction to computational methods in mathematical modeling, including linear programming and Markov chains. Applications in business, economics, and systems engineering. Knowledge of probability will be helpful.

331 Real Analysis 1 unit
Spring
Prerequisites: Mathematics 245 and either Mathematics 236 or 239.
A study of the concepts underlying calculus of a single variable: the completeness property of the real number system, convergence, continuity, properties of elementary functions, the derivative, and the Riemann integral.

335 Abstract Algebra 1 unit
Fall
Prerequisite: Mathematics 236 and 239.
Properties of the integers, real number system and other familiar algebraic entities are viewed abstractly in structures such as groups, semigroups, rings, and fields. Homomorphisms and isomorphisms (functions compatible with the algebraic operations) illuminate the underlying similarities among these structures. Students will develop their skills in mathematical writing and presentations.

342 Geometry 1 unit
Spring
Prerequisites: Mathematics 143 and 239.
The logical foundations of Euclidean geometry, including the axiom systems of Euclid and Hilbert, and their philosophical implications. An introduction to hyperbolic, elliptic, and projective geometry. Students will use software such as Geometer’s Sketchpad to illustrate and motivate course topics.

345 History of Mathematics 1 unit
Fall of odd-numbered years
Prerequisite: Mathematics 141.
A study of the history and evolution of mathematical ideas and their significance, from approximately 3500 BCE to the present. Topics include number systems, arithmetic, Euclidean and non-Euclidean geometry, algebra, calculus, probability, number theory, and applied mathematics.

360 Mathematical Modeling 1 unit
Spring of even-numbered years
Prerequisites: Mathematics 236 and Computer Science 171.
An introduction to analytical methods in mathematical modeling, including nonlinear optimization, dynamical systems and random processes. Applications in physics, biology, economics, and systems engineering. Knowledge of probability and statistics will be helpful.

380 Mathematical Physics 1 unit
Spring of even-numbered years.
Prerequisites: Physics 222 or 168, and Mathematics 247, 236, 245 or permission of instructor.
Mathematical methods in physics including vector calculus, transform calculus, tensor analysis, and special functions (viz. Fourier series, Gamma functions, Hermite polynomials, Bessel functions, spherical harmonics, and Laguerre polynomials). Same as Physics 380.

388, 389 Topics 1/2 or 1 unit
Fall, Spring
Prerequisite: Permission of instructor.
Topics chosen to fit departmental interests, such as complex variables, mathematical logic, geometric topology, chaos and fractals, number theory, algebraic coding theory, experimental design, nonparametric statistics, and stochastic processes. Offered on demand.

391, 392 Internship 1/2 or 1 unit
Fall, Spring
Offered on a credit/no credit basis.

399 Colloquium in Mathematics & Computer Science II 1/4 unit
Fall, Spring
Offered only on a credit/no credit basis.
Prerequisite: Mathematics/Computer Science 299 and senior standing.
Selected topics in mathematics and computer science as presented by students, departmental faculty and visiting speakers. In addition to submitting written summaries of each presentation, students take a departmental major assessment examination, and give an oral presentation on a mathematics/computer science topic of personal interest.

401, 402 Seminar 1/2 or 1 unit
Fall, Spring

411, 412 Directed Study 1/2 or 1 unit
Fall, Spring

Math 094 Essential Mathematics with Elementary Algebra (4 credits)

Basic mathematics skills integrating the fundamental operations of whole numbers, integers, fractions, decimals, percents, ratio and proportion with the elementary algebra topics of linear equations and inequalities, graphs, exponents, polynomials and factoring. Credit does not apply toward graduation.

Math 098 Intermediate Algebra (4 credits)

Topics covered include intermediate study of graphs, systems of linear equations, introduction to functions, linear and nonlinear inequalities, factoring, rational expressions and equations, radicals, and basic quadratic equations. Credit does not apply toward graduation.

Math 110 Perspectives in Mathematics (3 credits)

A survey of mathematics and its relationship to society, showing its development and evolution to meet the needs of humanity. Pre: Two years high school algebra and/or geometry.

Math 112 College Algebra (4 credits)

Concepts of algebra (real numbers, exponents, polynomials, rational expressions), equations and inequalities, functions and graphs, polynomial and rational functions, exponential and logarithmic functions, systems of equations and inequalities, matrices and determinants, conic sections, sequences and series, probability, and binomial theorem. Pre: Scoring 18 or better on the Intermediate Algebra Placement Test, or scoring 19 or better on the ACT Math Subscore, or successful completion of Math 098.

Math 113 Trigonometry (3 credits)

Basic concepts of trigonometry as preparation for college level mathematics and science courses. Topics include concepts of algebra (real numbers, functions, graphs of functions, exponential and logarithmic functions), trigonometric functions, analytic trigonometry, applications of trigonometry, and analytic geometry. Pre: Scoring 18 or better on the Intermediate Algebra Placement Test, or scoring 6 or better on the Functions and Graphs Placement Test, or scoring 19 or better on the ACT Math Subscore, or Math 112 with C or better.

Math 115 Precalculus Mathematics (4 credits)

This course is designed for students preparing to take calculus who need a review of algebra and trigonometry. Topics include functions, graphs of functions, exponential and logarithmic functions, conic sections, systems of equations and inequalities, matrices, trigonometric functions, circular functions, vectors and complex numbers, induction, series and probability. Pre: Scoring 19 or better on the Intermediate Algebra Placement Test, or scoring 6 or better on the Functions and Graphs Placement Test, or scoring 20 or better on the ACT Math Subscore.

Math 121 Calculus I (4 credits)

Limits, continuity, the derivative and its applications, and the integral and its applications. Pre: Scoring 16 or better on the Functions and Graphs Placement Test with 6 or better on Trigonometry, or scoring 22 or better on the ACT Math Subscore, or Math 112 and Math 113 with C or better, or Math 115 with C or better.

Math 122 Calculus II (4 credits)

Definite integral and applications, transcendental functions, L’Hopital’s rule, techniques of integration, sequences and series, parametric equations, polar coordinates, and vectors in two and three dimensions. Pre: Math 121 with C or better or consent.

Math 127 Calculus II for Engineering Technology: Integration (2 credits)

A continuation of the study of calculus from Math 121 including definite integral and applications, transcendental functions, L’Hopital’s rule, techniques of integration, and vectors in two and three dimensions. Content is intended for students enrolled in any engineering technology program. Credit for both Math 127 and Math 122 is not allowed. Pre: Math 121 with C or better or consent.

Math 128 Calculus II for Engineering Technology: Infinite Series (2 credits)

A continuation of the study of calculus from Math 127 including infinite series, parametric equations, and polar coordinates. Content is intended for students enrolled in any engineering technology program. Credit for both Math 128 and Math 122 is not allowed. Pre: Math 127 with C or better or consent.

Math 130 Finite Mathematics and Its Applications (3 credits)

This course introduces the mathematical concepts needed in business, the social sciences and the life sciences including problem solving, linear models, linear algebra, linear programming, consumer mathematics, probability and statistics, and decision making. Pre: Three years of high school mathematics.

Math 180 Mathematics for Computer Science (4 credits)

This course introduces the mathematical concepts needed in computer science, including sets, logic, representations of numbers, counting techniques, discrete functions, matrices, trees and graphs, and algorithm analysis. Pre: Math 112 or equivalent.

Math 181 Intuitive Calculus (3 credits)

This course presents the concepts of the differential and integral calculus from an intuitive (non-theoretical) point of view. The course emphasis is on the applications of the calculus to the fields of business and economics. Pre: Math 112 or equivalent.

Math 201 Elements of Mathematics I (3 credits)

Nature of mathematics from a problem solving approach using sets, relations, number systems through integers, rational numbers and discrete mathematics. Pre: Scoring 18 or better on the Intermediate Algebra Placement Test, or scoring 19 or better on the ACT Math Subscore, or successful completion of Math 098.

Math 202 Elements of Mathematics II (3 credits)

A continuation of Math 201 including rational and real number systems, informal geometry and measurement, statistics and probability. Pre: Math 201.

Math 223 Calculus III (4 credits)

Surfaces, vector-valued functions, partial differentiation, multiple integration, and vector calculus. Pre: Math 122 with C or better or consent.

Math 247 Linear Algebra I (4 credits)

Matrices, determinants, systems of linear equations, vector spaces, linear transformations, and characteristic value problems. Pre: Math 122.

Math 290 Foundations of Mathematics (4 credits)

Logic, proof techniques, set theory, relations, functions, cardinality, operations, and an introduction to mathematical structures and number theory. Pre: Math 247.

Math 303 Elements of Mathematics III (3 credits)

A continuation of Math 202, including transformational and Euclidean geometry, coordinate geometry and applications of discrete mathematics. Pre: Math 202.

Math 316 Intermediate Analysis (3 credits)

Limits, sequences, continuity, and differentiation of a real valued function of a real variable. Pre: Math 223 and 290.

Math 321 Ordinary Differential Equations (4 credits)

This course presents the theory, computations, and applications of first and second order differential equations and two-dimensional systems. Pre: Math 122.

Math 332 College Geometry (4 credits)

Geometric systems including Euclidean, non-Euclidean, transformational and projective, as well as topological properties and the relationship between coordinate and synthetic geometry. Pre: Math 290.

Math 345 Abstract Algebra I (4 credits)

An introduction to the theory of groups and rings, including polynomial rings, homomorphisms, isomorphisms, and concepts of normal subgroups, ideals, quotient groups, and quotient rings. Pre: Math 290.

Math 354 Concepts of Probability and Statistics (3 credits)

This is a calculus-based course covering introductory level topics of probability and statistics. It is designed to meet the needs of both the practitioner and the person who plans further in-depth study. Topics include probability, random variables and probability distributions, joint probability distributions, statistical inference (both estimation and hypothesis testing), analysis of variance, regression, and correlation. Same as Stat 354. Pre: Math 122.

Math 375 Introduction to Discrete Mathematics (4 credits)

An introduction to the concepts fundamental to the analysis of algorithms and their realization. Topics will include combinatorics, generating functions, recurrence relations, graph theory, and networks. Pre: Math 247 or consent.

Math 392 Topology of Euclidean Spaces (4 credits)

Metric spaces, topology of metric spaces, continuity, compactness in metric spaces, and Euclidean n-space. Pre: Math 290.

Math 411 Introduction to Complex Variables (4 credits)

Algebra and geometry of complex numbers, analytic functions, power series, Cauchy’s theorem and residue theorem. Pre: Math 223 and 290.

Math 417 Real Analysis I (3 credits)

Limits and continuity, sequences and series, differentiation and integration. Pre: Math 223 and 290.

Math 418 Real Analysis II (3 credits)

Topology of Euclidean spaces, continuous functions, sequences of functions and differentiable mappings. Pre: Math 417.

Math 422 Partial Differential Equations (4 credits)

This course presents the theory, computations, and applications of partial differential equations and Fourier series. Pre: Math 223 and 321.

Math 425 Mathematical Modeling (4 credits)

This course presents topics from mathematical analysis of both discrete and continuous models taken from problems in the natural sciences, economics and resource management. Pre: Math 223 and 247.

Math 435 Modern Geometry (4 credits)

Geometry of spaces including Euclidean and non-Euclidean and applications of contemporary geometry. Pre: Math 332 or consent.

Math 442 Theory of Numbers (4 credits)

Euclidean algorithm, primes, composites, number theoretic functions, congruencies, Diophantine equations, Euler and Fermat theorems, algebraic number fields. Pre: Math 345.

Math 446 Abstract Algebra II (4 credits)

A continuation of Math 345. The course will include topics from groups, rings, and fields. Pre: Math 345.

Math 447 Linear Algebra II (3 credits)

An in-depth study of linear operators and their related spaces, dimension, rank, matrix representation of linear operators, special matrices, determinants, eigenvectors and eigenvalues. Pre: Math 345.

Math 455 Theory of Statistics I (4 credits)

A mathematical approach to statistics with derivation of theoretical results and of basic techniques used in applications. Includes probability, continuous probability distributions, multivariate distributions, functions of random variables, central limit theorem and statistical inference. Same as Stat 455. Pre: Math 223.

Math 456 Theory of Statistics II (4 credits)

A mathematical approach to statistics with derivation of theoretical results and of basic techniques used in applications, including sufficient statistics, additional statistical inference, theory of statistical tests, inferences about normal models and nonparametric methods. Same as Stat 456. Pre: Math/Stat 455.

Math 470 Numerical Analysis I (4 credits)

This course provides an introduction to techniques and analysis involved with solving mathematical problems using technology. Topics included are errors in computation, solutions of linear and nonlinear equations, numerical differentiation and integration, and interpolation. Pre: Math 122 and 247.

Math 471 Numerical Analysis II (4 credits)

This course is a continuation of Math 470. Topics included are the algebraic eigenvalue problem, least-squares approximation, solutions of systems of nonlinear equations, numerical solutions of ordinary differential equations. Pre: Math 470, 223.

Math 480 History of Mathematics (3 credits)

The development of selected topics from before the Hellenistic time period to the late twentieth century. Familiarity with the content of Hist 180 is beneficial. Pre: Math 345.

Math 483 Advanced Viewpoint of 5-8 School Mathematics (3 credits)

Advanced viewpoint of mathematical content, theories of learning, teaching strategies, reading strategies, assessments and planning for teaching mathematics in grades 5-8. Pre: Math 290.

Math 484 Technology in 5-12 School Mathematics (2 credits)

This course is designed to inform secondary mathematics teachers about effective utilization of technology in the mathematics curriculum. Pre: Math 345.

Math 485 Teaching Secondary School Mathematics (3 credits)

This course is designed to inform the prospective secondary mathematics teacher about current trends and issues, and instructional techniques and materials. Pre: Math 345.

Math 487 Teaching Experiences in Mathematics (1 credit)

Student will work with an experienced member of the faculty in teaching a college mathematics course.

Math 488 Seminar (1-3 credits)

A course of study in which a group of students study a topic by examining results through reports and discussions. May be repeated for credit on each new topic.

Math 490 Workshop (1-4 credits)

A short course devoted to a specific mathematical topic. May be repeated for credit on each new topic.

Math 491 Inservice (1-4 credits)

A course designed to upgrade the qualifications of persons on-the-job. May be repeated for credit on each new topic.

Math 492 Mathematics Capstone Experience (3 credits)

This course is designed to allow undergraduate students an opportunity to integrate their mathematical experiences by working on a problem in applied or theoretical mathematics. Content will vary by semester. The course can also be taken as an independent study with permission of a cooperating faculty member. Pre: Senior standing and two of the following three courses – Math 316, 345, 375.

Math 495 Selected Topics (1-4 credits)

A course in an area of mathematics not regularly offered. May be repeated for credit on each new topic.

Math 496 Mathematical Logic (3 credits)

Propositional logic, first and second order logic, completeness, consistency, models of theories, Godel’s Incompleteness theorem. Pre: Math 345.

Math 498 Internship (1-12 credits)

Provides a student the opportunity to gain expertise and experience in a special field under the supervision of a qualified person.

Math 499 Individual Study (1-4 credits)

Independent individual study under the guidance and direction of a faculty member in mathematics. Special arrangements must be made with an appropriate faculty member. May be repeated for credit on each new topic.