# MATH - Mathematics

*Christopher Williams, Interim Dept. Chair, Dept. of Mathematics (300 Carol Ryrie Brink Hall 83844-1103; phone 208/885-6742).*

**Vertically-related courses in this subject field are:** MATH 170-MATH 175-MATH 275-MATH 471-MATH 472.

**Credit Limitations:** MATH 108 carries no credit after MATH 137 or MATH 143; MATH 137 carries no credit after MATH 143; MATH 143 carries no credit after MATH 160 or MATH 170; MATH 170 carries 2 credits after MATH 160; MATH 160 carries no credit after MATH 170, MATH 215 carries no credit after MATH 461 or MATH 471.

## MATH 108 Intermediate Algebra

**Math 108 Intermediate Algebra (3 cr)**

Carries no credit after Math 137 or 143. Review of algebra including factoring, rational expressions, exponents, radicals, quadratic equations, equations of lines. Taught using the Polya Math Center, a studio environment featuring group study, one-to-one interaction with instructors, computer-mediated modules, and lectures. Does not satisfy general education requirement..

## MATH 123 Mathematics Applied to the Modern World

**Math 123 Mathematics Applied To The Modern World (3 cr)**

*Gen Ed: Mathematics*

Discussion of some aspects of mathematical thought through the study of problems taken from areas such as logic, political science, management science, geometry, probability, and combinatorics; discussion of historical development and topics discovered in the past 100 years.

## MATH 130 Finite Mathematics

**Math 130 Finite Mathematics (3 cr)**

*Gen Ed: Mathematics*

Systems of linear equations and inequalities, matrices, linear programming, and probability.

* Prereq:* Sufficient score on SAT, ACT, or math placement test; or Math 108 with a "C" or better. Required test scores can be found here: http://www.uidaho.edu/registrar/registration/placement.

## MATH 137 Algebra with Applications

**Math 137 Algebra with Applications (3 cr)**

Carries no credit after Math 143. Algebraic, exponential, logarithmic functions, systems of equations, applications.

* Prereq:* A grade of "C" or better in Math 108 or sufficiently high score on SAT, ACT, or math placement test. It is recommended that Math 137 be taken within two years of passing Math 108 or its equivalent. Math 137 is not sufficient preparation for Math 170. Students intending to take Math 170 should enroll in Math 143 instead. Required test scores can be found here: http://www.uidaho.edu/registrar/registration/placement.

## MATH 143 Pre-calculus Algebra and Analytic Geometry

**Math 143 Pre-calculus Algebra and Analytic Geometry (3 cr)**

*Gen Ed: Mathematics*

Carries no credit after Math 160 or Math 170; carries 2 credits after Math 137. Algebraic, exponential, logarithmic functions; graphs of conics; zeros of polynomials; systems of equations, induction. Taught using the Polya Math Center, a studio environment featuring group study, one-to-one interaction with instructors, computer-mediated modules, and lectures.

* Prereq:* Sufficient score on SAT, ACT, or math placement test; or Math 108 with grade of "C" or better. It is recommended that Math 143 be taken within two years of passing Math 108 or its equivalent. Required test scores can be found here: http://www.uidaho.edu/registrar/registration/placement

## MATH 144 Analytic Trigonometry

**Math 144 Analytic Trigonometry (1 cr)**

Not open for cr to students who have previous high school or college cr in trigonometry. Trigonometric functions, inverse functions, applications. Taught using the Polya Math Center, a studio environment featuring group study, one-to-one interaction with instructors, computer-mediated modules, and lectures.

* Prereq:* Sufficient score on SAT, ACT, or math placement test. Students may qualify by enrolling concurrently in Math 143 or Math 170. Required test scores can be found here: http://www.uidaho.edu/registrar/registration/placement.

## MATH 160 Survey of Calculus

**Math 160 Survey of Calculus (4 cr)**

*Gen Ed: Mathematics*

Carries no credit after Math 170. Overview of functions, and graphs, derivatives, integrals, exponential and logarithmic functions, functions of several variables, and differential equations. Primarily for students who need only one semester of calculus, such as students in business or architecture.

* Prereq:* Sufficient score on SAT, ACT, or math placement test, or Math 137 with a "C" or better, or Math 143 with a "C" or better. Required test scores can be found here: http://www.uidaho.edu/registrar/registration/placement.

## MATH 170 Analytic Geometry and Calculus I

**Math 170 Analytic Geometry and Calculus I (4 cr)**

*Gen Ed: Mathematics*

Carries 2 credits after Math 160. Functions, limits, continuity, differentiation, integration, applications, differentiation and integration of transcendental functions. Primarily for students in engineering, mathematics, science or computer science.

* Prereq:* Math 143 (with a grade of "C" or better) and Math 144 (concurrent enrollment in Math 144 is allowed although it is recommended that students complete Math 144 before enrolling in Math 170); or demonstrated proficiency through a sufficiently high score on the ACT, SAT, or math placement test. Required test scores can be found here: http://www.uidaho.edu/registrar/registration/placement.

## MATH 175 Analytic Geometry and Calculus II

**Math 175 Analytic Geometry and Calculus II (4 cr)**

*Gen Ed: Mathematics*

Differentiation and integration of transcendental functions, integration techniques, general mean value theorem, numerical techniques, and series.

* Prereq:* Math 170 with a grade of "C" or better

## MATH 176 Discrete Mathematics

**Math 176 Discrete Mathematics (3 cr)**

Induction, set theory, graph theory, number systems, Boolean algebra, and elementary counting.

* Prereq:* Math 143 or sufficiently high score on SAT, ACT, or math placement test. Required test scores can be found here: http://www.uidaho.edu/registrar/registration/placement.

## MATH 204 Special Topics

**Math 204 (s) Special Topics (cr arr)**

## MATH 215 Proof via Number Theory

**Math 215 Proof via Number Theory (3 cr) **

An introduction to mathematical thinking and proof through the development of the basic results of elementary number theory. Emphasis on techniques of mathematical proofs, reading and writing proofs, and fundamental mathematical structures.

* Prereq:* Math 175 and Math 176

## MATH 275 Analytic Geometry and Calculus III

**Math 275 Analytic Geometry and Calculus III (3 cr)**

*Gen Ed: Mathematics*

Vectors, functions of several variables, and multiple integration.

* Prereq:* Math 175

## MATH 299 Directed Study

**Math 299 (s) Directed Study (cr arr)**

## MATH 310 Ordinary Differential Equations

**Math 310 Ordinary Differential Equations (3 cr)**

Classification, initial and boundary value problems of one variable, exact equations, methods of solving higher-order linear equations, second-order equations with constant coefficient, series solutions, systems of linear equations, Laplace transforms, and existence theorems. Recommended preparation: Math 275.

* Prereq:* Math 175

## MATH 315 HON:Topics in Pure Mathematics

**Math H315 Topics in Pure Mathematics (3 cr)**

A topic selected each yr that develops skill and appreciation for theoretical nature of mathematics.

* Prereq:* Permission of director of University Honors Program

## MATH 326 Linear Optimization

**Math 326 Linear Optimization (3 cr) **

Geometric solutions, simplex method, duality and revised simplex method, sensitivity, integer programming, applications. Recommended Preparation: Math 175.

* Prereq:* Math 160 or 170

## MATH 330 Linear Algebra

**Math 330 Linear Algebra (3 cr)**

Linear equations, matrices, linear transformations, eigenvalues, diagonalization; applications. Recommended Preparation: Math 175.

* Prereq:* Math 160 or 170

## MATH 371 Mathematical Physics

**Math 371 Mathematical Physics (3 cr)**

See Phys 371.

## MATH 376 Discrete Mathematics II

**Math 376 Discrete Mathematics II (3 cr)**

Selected topics from discrete mathematics such as graph theory, modeling, and optimization. Recommended for computer science majors.

* Prereq:* Math 176 or Permission

## MATH 385 Theory of Computation

**Math 385 Theory of Computation (3 cr)**

Same as CS 385. Mathematical models of computation, including finite automata and Turing machines. (Fall only)

* Prereq:* Permission

## MATH 386 Theory of Numbers

**Math 386 Theory of Numbers (3 cr)**

Second course on number theory, including a historical treatment of efforts to answer basic questions on the density and possible forms of prime numbers. Topics may include: quadratic reciprocity, cubic reciprocity, quadratic forms, genus theory, higher reciprocity laws, Hilbert class field, the prime number theorem, Dirichlet's theorem on primes in an arithmetic progression, elliptic curves, and modular forms.

**Prereq:** Math 215

## MATH 388 History of Mathematics

**Math 388 History of Mathematics (3 cr)**

Same as Hist 388. History of the development of mathematical ideas from ancient cultures to the present, including the relationship of those ideas to the cultures that produced them as well as an understanding of the mathematics involved. Cooperative: open to WSU degree-seeking students.

* Prereq:* Math 175 or Permission

## MATH 390 Axiomatic Geometry

**Math 390 Axiomatic Geometry (3 cr) **

*May be used as core credit in J-3-d.* Development of Euclidean and hyperbolic geometry using the axiomatic approach. Recommended Preparation: Math 215.

* Prereq:* High school geometry and Math 330, or Permission

## MATH 391 Modern Geometry

**Math 391 Modern Geometry (3 cr) **

Euclidean and non-Euclidean geometries, plus topics chosen from projective, transformational, and computational geometry. Recommended Preparation: Math 215.

* Prereq:* High School Geometry and Math 330, or Permission

## MATH 395 Analysis of Algorithms

**Math 395 Analysis of Algorithms (3 cr)**

Same as CS 395. Measures of efficiency; standard methods and examples in the design and analysis of algorithms. (Spring only)

* Prereq:* Math 175

## MATH 400 Seminar

**Math 400 (s) Seminar (cr arr)**

## MATH 404 Special Topics

**Math 404 (s) Special Topics (cr arr)**

## MATH 415 Cryptography

**Math 415 Cryptography (3 cr)**

*Gen Ed: Senior Experience*

Congruences, modular arithmetic, private-key cryptosystems, public-key cryptosystems, and applications. The role of modern mathematics in information age society.

* Prereq:* Math 330

## MATH 420 Complex Variables

**Math 420 Complex Variables (3 cr) **

Complex numbers, elementary functions, derivatives, the residue theorem, conformal mappings, contour integration, infinite series, applications.

* Prereq:* Math 275

## MATH 426 Discrete Optimization

**Math 426 Discrete Optimization (3 cr)**

Optimization on graphs, networks and flows, and related topics. Recommended Preparation: Math 175.

## MATH 427 Transformational Geometry

**Math 427 Transformational Geometry (3 cr)**

See MthE 527.

## MATH 428 Numerical Methods

**Math 428 Numerical Methods (3 cr)**

See Phys J428/J528.

## MATH 430 Advanced Linear Algebra

**Math 430 Advanced Linear Algebra (3 cr)**

Vector spaces, linear transformations, characteristic polynomial, eigenvectors, Hermitian and unitary operators, inner products, quadratic forms, Jordan canonical form, applications. Recommended Preparation: Math 215.

* Prereq:* Math 330 or Permission

## MATH 432 Numerical Linear Algebra

**Math 432 Numerical Linear Algebra (3 cr)**

Analysis of efficiency and accuracy of large linear algebra problems; special emphasis on solving linear equations and finding eigenvalues.

* Prereq:* Math 275, 330, and knowledge of a computer language

## MATH 435 Topics in Applied Mathematics

**Math 435 (s) Topics in Applied Mathematics (cr arr)**

Topics chosen from fields of current interest in applied mathematics; inquire at the Department of Mathematics for a description of topics for future semesters.

* Prereq:* Permission

## MATH 437 Mathematical Biology

**Math 437 Mathematical Biology (3 cr)**

Modeling biological phenomena, mostly through differential equations; mathematical topics include stability analysis and limit cycles for nonlinear ODE's, spatial diffusion and traveling waves for PDE's; biological topics include models of predator-prey systems, infectious diseases, and competition. Cooperative: open to WSU degree-seeking students.

* Prereq:* Math 310 or Permission

## MATH 438 Mathematical Modeling

**Math 438 Mathematical Modeling (3 cr)**

Topics in the use of mathematics to model phenomena from science, business, economics, and engineering.

**Prereq:** Math 310 and Math 330

## MATH 451 Probability Theory

**Math 451 Probability Theory (3 cr)**

Same as Stat 451. Random variables, expectation, special distributions (normal, binomial, exponential, etc.), moment generating functions, law of large numbers, central limit theorem. Cooperative: open to WSU degree-seeking students. (Fall only)

* Prereq:* Math 275, or Permission

* Coreq:* Math 275

## MATH 452 Mathematical Statistics

**Math 452 Mathematical Statistics (3 cr)**

Same as Stat 452. Estimation of parameters, confidence intervals, hypothesis testing, likelihood ratio test, sufficient statistics. Cooperative: open to WSU degree-seeking students. (Spring only)

* Prereq:* Math 451 or Permission

## MATH 453 Stochastic Models

**Math J453/J538 Stochastic Models (3 cr)**

Same as Stat J453/J544. Markov chains, stochastic processes, and other stochastic models; applications. Additional projects/assignments required for graduate credit. Cooperative: open to WSU degree-seeking students.

* Prereq:* Math 451 or Permission

## MATH 455 Applied Actuarial Science II

**Math 455 Applied Actuarial Science (1 cr)**

Risk problems on the actuarial exam. Graded P/F.

* Prereq:* Math 451

## MATH 461 Abstract Algebra I

**Math 461 Abstract Algebra I (3 cr) **

Groups, rings, and fields. (Fall only)

* Prereq:* Math 215 and Math 330; or Permission

## MATH 462 Abstract Algebra II

**Math 462 Abstract Algebra II (3 cr)**

Groups, rings, and fields. (Spring only)

* Prereq:* Math 461

## MATH 471 Introduction to Analysis I

**Math 471 Introduction to Analysis I (3 cr)**

Topology of Euclidean n-space, limit and continuity, differentiation, integration. (Fall only)

* Prereq:* Math 275 and Math 215; or Permission

## MATH 472 Introduction to Analysis II

**Math 472 Introduction to Analysis II (3 cr) **

Topology of Euclidean n-space, limit and continuity, differentiation, integration. (Spring only)

* Prereq:* Math 471 or Permission

## MATH 476 Combinatorics

**Math 476 Combinatorics (3 cr)**

Elementary counting methods, generating functions, recurrence relations, Polya's enumeration, enumeration of graphs, trees, searching, combinatorial algorithms. Recommended Preparation: Math 176, or 215, or 376.

* Prereq:* Math 175 and 330

## MATH 480 Partial Differential Equations

**Math 480 Partial Differential Equations (3 cr)**

Intro to Fourier analysis, application to solution of partial differential equations; classical partial differential equations of engineering and physics.

* Prereq:* Math 310 or Permission

## MATH 494 Seminar in Mathematical Biology

**Math 494 Seminar in Mathematical Biology (1 cr)**

Oral presentation of research approaches, research results and literature review of mathematical biology including mathematical modeling of biological systems. Cooperative: open to WSU degree-seeking students.

## MATH 499 Directed Study

**Math 499 (s) Directed Study (cr arr)**

## MATH 500 Master's Research and Thesis

**Math 500 Master's Research and Thesis (cr arr)**

## MATH 501 Seminar

**Math 501 (s) Seminar (cr arr)**

## MATH 502 Directed Study

**Math 502 (s) Directed Study (cr arr)**

## MATH 504 Special Topics

**Math 504 (s) Special Topics (cr arr)**

## MATH 505 Professional Development

**Math 505 (s) Professional Development (cr arr)**

Cr earned in this course will not be accepted toward grad degree programs.

* Prereq:* Permission

## MATH 510 Seminar on College Teaching of Mathematics

**Math 510 Seminar on College Teaching of Mathematics (1 cr)**

Development of skills in the teaching of college mathematics; includes structure of class time, test construction, and various methods of teaching mathematics; supervision of teaching assistants in their beginning teaching assignments. Graded P/F.

* Prereq:* Permission

## MATH 521 Topology I

**Math 521 Topology I (3 cr)**

Basic concepts of point set and algebraic topology. Cooperative: open to WSU degree-seeking students.

## MATH 522 Topology II

**Math 522 Topology II (3 cr) **

Basic concepts of point set and algebraic topology.

## MATH 523 Algebraic Topology I

**Math 523 Algebraic Topology I (3 cr) **

Basic homotopy theory, covering spaces, homology theory, and applications.

## MATH 528 Differentiable Manifolds

**Math 528 Differentiable Manifolds (3 cr)**

Fundamentals of smooth manifolds, tangent spaces, vector fields, Lie groups, integration on manifolds, and applications. Cooperative: open to WSU degree-seeking students.

**Prereq:** Math 521 and Math 472

## MATH 531 Complex Variables

**Math 531 Complex Variables (3 cr)**

Theory of functions of a complex variable. Cooperative: open to WSU degree-seeking students.

## MATH 535 Real Variables

**Math 535 Real Variables (3 cr)**

Measure and integration theory for functions of one or several variables.

## MATH 536 Probability Theory

**Math 536 Probability Theory (3 cr)**

Random variables, characteristic functions, convergence theorems, central limit theorem, conditional probability, and stochastic processes as developed from a measure theoretic basis.

* Prereq:* Math 535 or Permission

## MATH 538 Stochastic Models

**Math 538 Stochastic Models (3 cr)**

See Math J453/J538.

## MATH 539 Theory of Ordinary Differential Equations

**Math 539 Theory of Ordinary Differential Equations (3 cr)**

Existence, uniqueness, and stability of solutions of first-order systems; other topics. Cooperative: open to WSU degree-seeking students.

## MATH 540 Partial Differential Equations

**Math 540 Partial Differential Equations (3 cr)**

Existence and uniqueness theorems for the wave, heat, and Laplace's equations of physics; additional topics such as nonlinear models in mathematical biology, perturbation methods, etc. Cooperative: open to WSU degree-seeking students.

* Prereq:* Math 539 or Permission

## MATH 541 Seminar in Analysis

**Math 541 (s) Seminar in Analysis (1-3 cr, max arr)**

Current literature. Cooperative: open to WSU degree-seeking students.

## MATH 543 Approximation Theory

**Math 543 Approximation Theory (3 cr)**

Cooperative: open to WSU degree-seeking students.

## MATH 555 Groups and Fields I

**Math 555 Groups and Fields I (3 cr)**

Groups, fields, polynomials, Galois theory, representation theory. Cooperative: open to WSU degree-seeking students.

* Prereq:* Math 461 and Math 462; or equivalent

## MATH 556 Groups and Fields II

**Math 556 Groups and Fields II (3 cr)**

Groups, fields, polynomials, Galois theory, representation theory. Cooperative: open to WSU degree-seeking students.

* Prereq:* Math 555 or Permission

## MATH 557 Ring Theory

**Math 557 Ring Theory (3 cr)**

Rings, ideals, modules, commutative algebra. Cooperative: open to WSU degree-seeking students.

* Prereq:* Math 461 and Math 462; or equivalent

## MATH 558 Introduction to Algebraic Geometry

**Math 558 Introduction to Algebraic Geometry (3 cr)**

Affine and projective varieties, morphisms, functions on varieties, birational maps, applications. Cooperative: open to WSU degree-seeking students.

* Prereq:* Math 557 or Permission

## MATH 561 Seminar In Algebra

**Math 561 (s) Seminar in Algebra (1-3 cr, max arr)**

Current literature.

## MATH 563 Mathematical Genetics

**Math 563 Mathematical Genetics (3 cr)**

Same as Biol 563. Investigation of aspects of evolutionary biology with an emphasis on stochastic models and statistical methods; topics include: diffusion methods in molecular evolution, gene genealogies and the coalescent, inferring coalescent times from DNA sequences, population subdivision and F statistics, likelihood methods for phylogenic inference, statistical hypothesis testing, the parametric bootstrap. Cooperative: open to WSU degree-seeking students.

* Prereq:* Math 160 or Math 170 and Stat 251 or Stat 301

## MATH 571 Functional Analysis I

**Math 571 Functional Analysis I (3 cr)**

Linear topological spaces and linear operators.

* Prereq:* Math 535

## MATH 572 Functional Analysis II

**Math 572 Functional Analysis II (3 cr) **

Linear topological spaces and linear operators.

* Prereq:* Math 571

## MATH 575 Graph Theory I

**Math 575 Graph Theory I (3 cr)**

Basic concepts and theorems; topics include trees and connectivity, eulerian and hamiltonian graphs, graph colorings, matchings, graph decomposition, and extremal graph theory.

## MATH 576 Graph Theory II

**Math 576 Graph Theory II (3 cr)**

Basic concepts and theorems; topics include trees and connectivity, eulerian and hamiltonian graphs, graph colorings, matchings, graph decomposition, and extremal graph theory.

* Prereq:* Instructor Permission

## MATH 578 Combinatorial Optimization

**Math 578 Combinatorial Optimization (3 cr)**

Optimization problems on graphs, network flow problems, complexity analysis of algorithmic solutions, and related topics.

## MATH 579 Combinatorics

**Math 579 Combinatorics (3 cr)**

Topics from enumerative combinatorics, design theory, extremal combinatorics and algebraic combinatorics.

## MATH 581 Sem In Combinatorics

**Math 581 (s) Seminar in Combinatorics (1-3 cr, max arr)**

## MATH 583 Seminar in Applied Mathematics

**Math 583 Seminar in Applied Mathematics (3 cr, max arr)**

Cooperative: open to WSU degree-seeking students.

## MATH 596 MAT Comp Exam

**Math 596 MAT Comp Exam (1 cr)**

Supervised preparation for the Master of Arts in Teaching comprehensive exam. Graded Pass/Fail.

## MATH 598 Internship

**Math 598 (s) Internship (cr arr)**

## MATH 599 Research

**Math 599 (s) Non-thesis Master's Research (cr arr)**

Research not directly related to a thesis or dissertation.

* Prereq:* Permission

## MATH 600 Doctoral Research and Dissertation

**Math 600 Doctoral Research and Dissertation (cr arr)**