your adventure in

Mathematics

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Undergraduate Study

For the undergraduate curriculum in liberal arts and sciences, major in mathematics, leading to the degree bachelor of science, see Liberal Arts and Sciences, Curriculum.

The program in mathematics offers training suitable for students planning to enter secondary school teaching, to work in mathematics and computation for industry or government, or to continue their studies in graduate school. Students may satisfy the major requirements in several ways, suitable for various career objectives. Graduates can construct rigorous arguments to demonstrate mathematical facts. They can communicate their mathematical methods to others and can justify their assumptions.

Traditional Program

The traditional program of study for mathematics majors gives students a thorough grounding in mathematics. Graduates understand a broad range of mathematical topics and are familiar with a broad range of mathematical models. They have skills for solving problems in diverse situations. The program allows flexibility for specialization, and students are encouraged to steer their education according to career objectives.

MATH 101Orientation in Mathematics1
MATH 165Calculus I4
MATH 166Calculus II4
MATH 201Introduction to Proofs3
MATH 265Calculus III4
MATH 317Theory of Linear Algebra3-4
or MATH 407 Applied Linear Algebra
MATH 301Abstract Algebra I3
MATH 414Analysis I3
MATH 266Elementary Differential Equations3-4
or MATH 267 Elementary Differential Equations and Laplace Transforms
One of the following:2
Undergraduate Seminar
Pre-Student Teaching Experience III: Mathematics 1
Additional Mathematics courses at the 300 level or above15
Total Credits45-47
1

C I 480C is available only for students seeking secondary school certification.

 The courses listed above must include one of the sequences:

MATH 301
MATH 302
Abstract Algebra I
and Abstract Algebra II
6
MATH 373
MATH 481
Introduction to Scientific Computing
and Numerical Methods for Differential Equations
6
MATH 304
MATH 314
Combinatorics
and Graph Theory
6
MATH 414
MATH 415
Analysis I
and Analysis II
6
MATH 435
MATH 436
Geometry I
and Geometry II
6

 Communication Proficiency requirement:

ENGL 150Critical Thinking and Communication3
ENGL 250Written, Oral, Visual, and Electronic Composition 23
One of the following: 33
Undergraduate Thesis 4
Business Communication
Free-Lance Writing for Popular Magazines
Creative Writing: Nonfiction
Proposal and Report Writing
Technical Communication
2

The college requires a grade of C or better.

3

with grade C- or better

4

 with Departmental approval

Mathematics Plus

The Mathematics Plus option is for students who wish to establish a clear strength in a field of application of mathematics. They obtain the mathematics major by pursuing study of mathematics, through the upper division level, complementary to their application area. This program makes double majors more feasible and is appropriate for students who plan on employment or graduate study in the application field. It is not intended for students who plan on graduate study in mathematics. For more information, see the mathematics department web site or consult an adviser in mathematics.

Secondary Education

For certification requirements for teaching of mathematics in grades 5-12, see the Mathematics Department and School of Education web sites or consult an adviser. 

Recommendations

The department strongly recommends that each student majoring in mathematics include in the program substantial supporting work beyond the minimum general education requirement of the college in one or more areas of application of mathematics, such as other mathematical sciences, engineering, natural science, economics or finance. Particularly useful are:

COM S 207Fundamentals of Computer Programming3
COM S 208Intermediate Computer Programming3
PHIL 207Introduction to Symbolic Logic3
PHYS 221Introduction to Classical Physics I5
PHYS 222Introduction to Classical Physics II5
STAT 201Introduction to Statistical Concepts and Methods4

It also recommends that students contemplating graduate study in mathematics acquire a reading knowledge of French, German, or Russian.

Credits Not Counted

Credits earned in the following cannot be counted toward graduation by mathematics majors:

MATH 104Introduction to Probability3
MATH 105Introduction to Mathematical Ideas3
MATH 140College Algebra3
MATH 143Preparation for Calculus4
MATH 145Applied Trigonometry3
MATH 150Discrete Mathematics for Business and Social Sciences3
MATH 151Calculus for Business and Social Sciences3
MATH 160Survey of Calculus4
MATH 181Calculus and Mathematical Modeling for the Life Sciences I4
MATH 182Calculus and Mathematical Modeling for the Life Sciences II4
MATH 195Mathematics for Elementary Education I3
MATH 196Mathematics for Elementary Education II3

Minor in Mathematics

The department offers a minor in mathematics, which may be earned by credit in the following:

MATH 201Introduction to Proofs3
MATH 265Calculus III4
One of the following
MATH 317Theory of Linear Algebra4
MATH 407Applied Linear Algebra3
One of the following
MATH 301Abstract Algebra I3
MATH 304Combinatorics3
MATH 314Graph Theory3
MATH 350Number Theory3
MATH 421Logic for Mathematics and Computer Science3
MATH 435Geometry I3
MATH 436Geometry II3
One of the following
MATH 266Elementary Differential Equations3
MATH 267Elementary Differential Equations and Laplace Transforms4
MATH 331Topology3
MATH 341Introduction to the Theory of Probability and Statistics I3
MATH 365Complex Variables with Applications3
MATH 373Introduction to Scientific Computing3
MATH 414Analysis I3

With 5-12 Teacher Certification

Freshman
FallCreditsSpringCredits
ENGL 1503MATH 1664
LIB 1601STAT 2014
MATH 1011C I 2043
MATH 1654C I 2191
PSYCH 2303C I 280L0.5
General Education6General Education6
 18 18.5
Sophomore
FallCreditsSpringCredits
MATH 2013MATH 266 or 267 - Differential Equations3-4
MATH 2654MATH 3174
ENGL 2503C I 3333
C I 2023COM S 107 or 207 - Programming3
General Education4General Education3
Take Praxis-I by October 1 2.5 GPA for Admission to Teacher Ed 
 17 16-17
Junior
FallCreditsSpringCredits
MATH 3013MATH 34223
MATH 3413MATH 3973
MATH 4353MATH 4363
C I 4063C I 280A2
Communication Choice13C I 4263
General Education3C I 3953
 18 17
Senior
FallCreditsSpringCredits
MATH 4143C I 417C14
MATH 4973 
C I 480C2 
SP ED 4013 
General Education4 
 15 14

Students in all ISU majors must complete a three-credit course in U.S. diversity and a three-credit course in international perspectives. Check (http://www.registrar.iastate.edu/courses/div-ip-guide.html) for a list of approved courses. Discuss with your adviser how the two courses that you select can be applied to your graduation plan.

LAS majors require a minimum of 120 credits, including a minimum of 45 credits at the 300/400 level. Three of the required 45 300+ level credits must be earned in a general education group outside the group of your major. You must also complete the LAS foreign language requirement and any high school unmet admissions requirements.

Students pursuing licensure to teach grades 5 – 12 must meet the general education and professional teacher education requirements established by the University Teacher Education Program. (Check http://www.education.iastate.edu/te/) for the requirements.

1

ENGL 302, 305, 309, or 314, or JL MC 201.

2

Recommended

Without Teacher Certification

Freshman
FallCreditsSpringCredits
MATH 1011MATH 1664
MATH 1654Social Science Choice3
ENGL 1503Arts & Humanities Choice3
LIB 1601Natural Science Choice3
Natural Science Choice3Electives2
Electives3 
 15 15
Sophomore
FallCreditsSpringCredits
MATH 2013MATH 2674
MATH 2654MATH 3174
Social Science Choice3ENGL 2503
Arts & Humanities Choice3Social Science Choice3
Electives2Electives1
 15 15
Junior
FallCreditsSpringCredits
MATH Two-Course Sequence13MATH Two-Course Sequence13
MATH 301 or 4143MATH 301 or 4143
Arts & Humanities Choice3Communication Choice23
Foreign Language/Electives4Foreign Language/Electives 
Natural Science Choice Electives2
 13 11
Senior
FallCreditsSpringCredits
MATH Choice, Level 300+3MATH Choice, Level 300+3
MATH 492 or MATH Choice, Level 300+2-3MATH 492 or MATH Choice, Level 300+2-3
Arts & Humanitites Choice3Electives9-10
Electives6-7 
 14-16 14-16

Students in all ISU majors must meet the U.S. Diversity and the International Perspectives requirements. Check (http://www.registrar.iastate.edu/courses/div-ip-guide.html) for a list of approved courses. These courses may be courses that apply to other requirements.

The LAS General Education requirements for Mathmatics majors are 12 credits Arts and Humanities, 8 credits Natural Science, and 9 credits Social Science from the approved lists:  http://www.las.iastate.edu/academics/generaldeducation/.

LAS majors require a minimum of 120 credits, including a minimum of 45 credits at the 300/400 level. Three of the required 45 300+ level credits must be earned in a general educational group outside the group of the major. Students must also meet the LAS foreign-language requirement and complete any unmet admission requirements.

1

Every mathematics major must complete at least one of the following sequences:

   a.  Algebra -- MATH 301 AND MATH 302
   b.  Analysis -- MATH 414 and MATH 415
   c.  Discrete -- MATH 304 and MATH 314
   d.  Geometry -- MATH 435 and MATH 436
   e.  Numerical -- MATH 373 and MATH 481

If you use 301/302 or 414/415, then add an additional MATH Elective (300+).

Note that some courses are taught only in fall or only in spring, so plan appropriately.

2

ENGL 302, 305, 309, or 314, or JL MC 201, or MATH 491.

Graduate Study

The department offers programs leading to a Master of Science or Doctor of Philosophy degree in mathematics or applied mathematics, as well as minor work for students whose major is in another department. The department also offers a program leading to the degree of Master of School Mathematics (M.S.M.).

Students desiring to undertake graduate work leading to the M.S. or Ph.D. degree should prepare themselves by taking several upper division mathematics courses. It is desirable that these credits include introduction to analysis and abstract algebra.

The M.S. degree requires a student to take at least 30 credit hours and to write a creative component or thesis.Additionally, students must pass a comprehensive oral examination over their coursework and their creative component or thesis. See the online Mathematics Graduate Handbook for specific requirements.

The Ph.D. degree requires a student to take 48 credit hours of coursework in addition to research hours, pass written qualifying examinations, pass an oral preliminary exam, and perform an original research project culminating in a dissertation which is defended by an oral exam. Ph.D. candidates must have at least one year of supervised teaching experience. See the on-line Mathematics Graduate Handbook for specific requirements.

The M.S.M. degree is primarily for in-service secondary mathematics teachers. Students desiring to pursue the M.S.M degree should present some undergraduate work in mathematics beyond calculus. Candidates for the M.S.M. degree must write an approved creative component and pass a comprehensive oral examination over their course work and their creative component.

Expand all courses

Courses

Courses primarily for undergraduates:

(4-0) Cr. 0. F.S.


For students who do not have adequate facility with topics from high school algebra or do not meet the algebra admission requirement. The course is divided into tracks of one- and two-semester lengths. For most students a diagnostic exam will determine which track must be taken. Students will receive a grade in MATH 25 or MATH 30 respectively depending on the level of material covered. Satisfactory completion of MATH 30 is recommended for students planning to take MATH 140, MATH 143, MATH 145, MATH 150, or MATH 151, while MATH 25 is sufficient for MATH 104, MATH 105, MATH 195, STAT 101 or STAT 105. Students must complete MATH 30 to remove a deficiency in the algebra admission requirement. Topics include signed numbers, polynomials, rational and radical expressions, exponential and logarithmic expressions, and equations. Offered on a satisfactory-fail basis only.

(4-0) Cr. 0. F.S.


Students should initially enroll in MATH 10. See description of MATH 10. Offered on a satisfactory-fail basis only.

(4-0) Cr. 0. F.S.


Students should initially enroll in MATH 10. See description of MATH 10. Offered on a satisfactory-fail basis only.

(1-0) Cr. 1. F.S.


For new majors. Campus resources and opportunities available to students. Careers and programs of study in mathematics. Mathematical reasoning, culture and resources. Description of main branches of mathematics. Offered on a satisfactory-fail basis only.

(3-0) Cr. 3. F.S.SS.

Prereq: Satisfactory performance on placement assessment, 2 years of high school algebra, 1 year of high school geometry
Permutations, combinations, probability, expected value, and applications. Either MATH 104 or MATH 150 may be counted toward graduation, but not both.

(3-0) Cr. 3. F.S.SS.

Prereq: Satisfactory performance on placement assessment, 2 years of high school algebra, 1 year of high school geometry.
Introduction to contemporary mathematics with an emphasis on use of mathematics to solve real world problems. Typical topics are the mathematics of voting, methods of fair division and apportionment, and elementary game theory.

(3-0) Cr. 3. F.S.


Inquiry-based approach to mathematics, emphasizing the art, history, and beauty of the subject. Typical topics are mathematics from art, music, puzzles, patterns, and reasoning.

(3-1) Cr. 3. F.S.SS.

Prereq: Satisfactory performance on placement assessment, 2 years of high school algebra, 1 year of high school geometry; or MATH 30.
Coordinate geometry, quadratic and polynomial equations, functions, graphing, rational functions, exponential and logarithmic functions, inverse functions, quadratic inequalities, systems of linear equations. Prepares students for MATH 160. Students in the College of Liberal Arts and Sciences may not count MATH 140 toward the General Education Requirements.

(4-0) Cr. 4. F.S.

Prereq: Satisfactory performance on placement assessment, 2 years of high school algebra, 1 year of high school geometry; or MATH 140.
Preparation for MATH 160, MATH 165, and MATH 181. Functions, graphing, basic trigonometry, logarithms, exponentials. Emphasis on co-variational reasoning. Students in the College of Liberal Arts and Sciences may not count MATH 143 toward General Education Requirements. Only one of MATH 143 and MATH 145 may count toward graduation.

(3-0) Cr. 3. F.S.

Prereq: Satisfactory performance on placement assessment, 2 years of high school algebra, 1 year of high school geometry; or minimum of C- in MATH 140.
Mathematical ideas regarding the conception of space. General trigonometry, with an emphasis on the calculation of lengths, areas, and angles. The Law of Sines and the Law of Cosines. Polar, cylindrical, and spherical coordinate systems. Conic sections and quadric surfaces. Students in the College of Liberal Arts and Sciences may not count MATH 145 toward the General Education Requirements. Only one of MATH 143 and MATH 145 may count toward graduation.

(2-1) Cr. 3. F.S.SS.

Prereq: Satisfactory performance on placement assessment, 2 years of high school algebra, 1 year of high school geometry
Linear equations and inequalities, matrix algebra, linear programming, discrete probability. Either MATH 104 or MATH 150 may be counted toward graduation, but not both.

(2-1) Cr. 3. F.S.SS.

Prereq: Satisfactory performance on placement assessment, 2 years of high school algebra, 1 year of high school geometry
Differential calculus, applications to max-min problems, integral calculus and applications. Will not serve as prerequisite for MATH 265 or MATH 266. Only one of MATH 151, MATH 160, the sequence MATH 165-MATH 166, or the sequence MATH 181-MATH 182 may be counted towards graduation.

(4-0) Cr. 4. F.S.

Prereq: Satisfactory performance on placement assessment, 2 years of high school algebra, 1 year of geometry; or MATH 143; or MATH 140
Analytic geometry, derivatives and integrals of elementary functions, simple differential equations, and applications. Will not serve as a prerequisite for MATH 265 or MATH 266. Only one of MATH 151, MATH 160, the sequence MATH 165-MATH 166, or the sequence MATH 181-MATH 182 may be counted towards graduation.

(4-0) Cr. 4. F.S.SS.

Prereq: Satisfactory performance on placement assessment, 2 years of high school algebra, 1 year of geometry, 1 semester of trigonometry; or MATH 143
Differential calculus, applications of the derivative, introduction to integral calculus. Only one of MATH 151 or MATH 160 or the sequence MATH 165-MATH 166, or the sequence MATH 181-MATH 182 may be counted towards graduation.

(4-0) Cr. 4. F.S.SS.

Prereq: Minimum of C- in MATH 165 or high math placement scores
Integral calculus, applications of the integral, infinite series, parametric curves and polar coordinates. Only one of MATH 151, MATH 160, the sequence MATH 165-MATH 166, or the sequence MATH 181-MATH 182 may be counted towards graduation.

(4-0) Cr. 4. F.

Prereq: Permission of instructor and MATH 165 or high math placement scores
Integral calculus, applications of the integral, infinite series, parametric curves, and polar coordinates. Additional material of a theoretical, conceptual, computational, or modeling nature. Some of the work may require more ingenuity than is required for MATH 166. Preference will be given to students in the University Honors Program. Only one of MATH 151 or MATH 160, the sequence MATH 165-MATH 166, or the sequence MATH 181-MATH 182 may be counted towards graduation.

(4-0) Cr. 4. F.S.

Prereq: Satisfactory performance on placement assessment, 2 years of high school algebra, 1 year of high school geometry, 1 semester of trigonometry; or MATH 143
Exponential and logarithm functions, difference equations, derivatives, and applications of the derivative. Examples taken from biology. Only one of MATH 151, MATH 160, the sequence MATH 165- MATH 166, or the sequence MATH 181-MATH 182 may be counted towards graduation.

(4-0) Cr. 4. S.

Prereq: MATH 181
Integration, first and second order differential equations, applications of the definite integral, introduction to multivariable calculus. Examples taken from biology. Only one of MATH 151, MATH 160, the sequence MATH 165-MATH 166, or the sequence MATH 181-MATH 182 may be counted towards graduation.

(2-2) Cr. 3. F.S.

Prereq: Satisfactory performance on placement assessment, 2 years high school algebra, 1 year of high school geometry, enrollment in elementary education or early childhood education
Whole number operations through analysis of properties, theoretical and hands-on models, mathematical analysis of elementary students’ thinking; standard and non-standard algorithms; structure of the decimal system; linear measurement; two- and three-dimensional geometric shapes and spatial sense; number theory; algebra as it relates to elementary curricula/teaching profession. Students in the College of Liberal Arts and Sciences may not count MATH 195 toward General Education Requirements.

(2-2) Cr. 3. F.S.

Prereq: Minimum of C- in MATH 195 and enrollment in elementary education or early childhood education.
Integer, fraction and decimal operations through analysis of properties, theoretical and hands-on models, mathematical analysis of elementary students’ thinking; standard and non-standard algorithms; two- and three-dimensional measurement; probability and statistics; proportional reasoning; algebra as it relates to elementary curricula/teaching profession.

(3-0) Cr. 3. F.S.

Prereq: MATH 166 or MATH 166H
Logic and techniques of proof including induction. Communicating mathematics. Writing proofs about sets, functions, real numbers, limits, sequences, infinite series and continuous functions.

(3-0) Cr. 3. F.S.SS.

Prereq: 2 semesters of calculus
Systems of linear equations, determinants, vector spaces, linear transformations, orthogonality, least-squares methods, eigenvalues and eigenvectors. Emphasis on applications and techniques. Only one of MATH 207 and MATH 317 may be counted toward graduation.

(4-0) Cr. 4. F.S.SS.

Prereq: Minimum of C- in MATH 166 or MATH 166H
Analytic geometry and vectors, differential calculus of functions of several variables, multiple integrals, vector calculus.

(4-0) Cr. 4. F.S.

Prereq: Permission of the instructor; and MATH 166 or MATH 166H
Analytic geometry and vectors, differential calculus of functions of several variables, multiple integrals, vector calculus. Additional material of a theoretical, conceptual, computational, or modeling nature. Some of the work may require more ingenuity than is required in MATH 265. Preference will be given to students in the University Honors Program.

(3-0) Cr. 3. F.S.SS.

Prereq: Minimum of C- in MATH 166 or MATH 166H
Solution methods for ordinary differential equations. First order equations, linear equations, constant coefficient equations. Eigenvalue methods for systems of first order linear equations. Introduction to stability and phase plane analysis.

(4-0) Cr. 4. F.S.SS.

Prereq: Minimum of C- in MATH 166 or MATH 166H
Same as MATH 266 but also including Laplace transforms and series solutions to ordinary differential equations.

(1-0) Cr. 1. F.S.SS.

Prereq: MATH 266
Laplace transforms and series solutions to ordinary differential equations. Together, MATH 266 and MATH 268 are the same as MATH 267.

(1-0) Cr. 1. F.S.SS.

Prereq: Familiarity with ordinary differential equations of first and second order, permission of department.
Systems portion of MATH 266 and MATH 267: Eigenvalue methods for systems of first order linear equations. Introduction to stability and phase plane analysis. For students supplementing transfer courses in differential equations in order to earn credit in MATH 266 or 267. Students with credit in MATH 266 or MATH 267 may not earn credit in MATH 269.

Cr. 1-3. Repeatable.

Prereq: Permission of the instructor.
Independent study.

Cr. 1-3. Repeatable.

Prereq: Permission of the instructor.
Independent study.

(2-2) Cr. 3. F.

Prereq: Enrollment in elementary education and minimum of C- in MATH 196
Mathematical reasoning and topics in Euclidean and non-Euclidean geometry, including transformations, congruence, and similarity; exploration of probability with simulations; linearity and connections to Calculus; fractals and fractal dimension.

(3-0) Cr. 3. F.S.

Prereq: MATH 166 or MATH 166H, MATH 317 or MATH 407, and grade of C- or better in MATH 201
Theory of groups. Homomorphisms. Quotient groups. Introduction to rings. Emphasis on writing proofs.

(3-0) Cr. 3. S.

Prereq: MATH 301
Theory of rings and fields. Introduction to Galois theory. Emphasis on writing proofs.

(3-0) Cr. 3. F.

Prereq: MATH 166 or MATH 166H; MATH 201 or experience with proofs
Enumeration strategies involving permutations, combinations, partitions, binomial coefficients, inclusion-exclusion principle, recurrence relations, generating functions. Additional topics selected from probability, algebraic combinatorics, and applications.

(3-0) Cr. 3. S.

Prereq: MATH 166 or MATH 166H; MATH 201 or experience with proofs
Structure and extremal properties of graphs. Topics are selected from: trees, networks, colorings, paths and cycles, connectivity, planarity, directed graphs, matchings, Ramsey theory, forbidden structures, enumeration, applications.

(4-0) Cr. 4. F.S.

Prereq: Credit or enrollment in MATH 201
Systems of linear equations, determinants, vector spaces, inner product spaces, linear transformations, eigenvalues and eigenvectors. Emphasis on writing proofs and results. Only one of MATH 207 and MATH 317 may be counted toward graduation.

(3-0) Cr. 3. Alt. F., offered even-numbered years.

Prereq: MATH 301
Set theory, metric spaces, topological spaces, continuity, connectedness, homeomorphisms, compactness, and topological invariants. Examples from surfaces, knots, and various abstract objects. Emphasis on writing proofs.

(Cross-listed with STAT). (3-0) Cr. 3. F.S.

Prereq: MATH 265 (or MATH 265H)
Probability; distribution functions and their properties; classical discrete and continuous distribution functions; multivariate probability distributions and their properties; moment generating functions; simulation of random variables and use of the R statistical package. Credit for both STAT 341 and STAT 447 may not be applied toward graduation.

(Cross-listed with STAT). (3-0) Cr. 3. F.S.

Prereq: STAT 341; MATH 207 or MATH 317
Transformations of random variables; sampling distributions; confidence intervals and hypothesis testing; theory of estimation and hypothesis tests; linear model theory; use of the R statistical package for simulation and data analysis.

(Cross-listed with COM S). (3-0) Cr. 3. S.

Prereq: MATH 201 or COM S 230
Divisibility, integer representations, primes and divisors, linear diophantine equations, congruences, and multiplicative functions. Applications to cryptography.

(3-0) Cr. 3. S.

Prereq: MATH 265
Functions of a complex variable, including differentiation, integration and series expansions, residues, evaluation of integrals, conformal mapping.

(3-0) Cr. 3. F.

Prereq: MATH 265
Vector and matrix programming and graphing in MATLAB for scientific applications. Polynomial interpolation and approximation. Systems of linear equations and numerical linear algebra. Numerical differentiation and integration. Newton methods for solving nonlinear equations and optimization in one and several variables. Fast Fourier transform. Emphasis on effective use of mathematical software and understanding of its strengths and limitations.

(3-0) Cr. 3. F.S.

Prereq: MATH 265 and one of MATH 266, MATH 267
Separation of variables methods for elliptic, parabolic, and hyperbolic partial differential equations. Topics from Fourier series, Sturm-Liouville theory, Bessel functions, spherical harmonics, and method of characteristics.

(2-2) Cr. 3. S.

Prereq: MATH 201, MATH 301
Coursework in university mathematics including calculus, abstract algebra, discrete mathematics, geometry, and other topics as it relates to teaching mathematics in grades 5-12.

Cr. R. Repeatable, maximum of 2 times. F.S.SS.

Prereq: Permission of the department cooperative education coordinator; junior classification
Required of all cooperative education students. Students must register for this course prior to commencing each work period.

(Dual-listed with MATH 507). (3-0) Cr. 3. F.

Prereq: MATH 317; or MATH 207 and experience writing proofs
Advanced topics in applied linear algebra including eigenvalues, eigenvalue localization, singular value decomposition, symmetric and Hermitian matrices, nonnegative and stochastic matrices, matrix norms, canonical forms, matrix functions. Applications to mathematical and physical sciences, engineering, and other fields.

(3-0) Cr. 3. F.S.SS.

Prereq: Minimum of C- in MATH 201
A careful development of calculus of functions of one real variable: real number properties, sequences and series, limits, continuity, differentiation, and integration.

(3-0) Cr. 3. S.

Prereq: MATH 414; MATH 265; and MATH 317 or MATH 407
Sequences and series of functions of a real variable, uniform convergence, power series, metric spaces, calculus of functions of two or more real variables.

(Cross-listed with COM S). (3-0) Cr. 3. S.

Prereq: MATH 301 or MATH 207 or MATH 317 or COM S 230
Propositional and predicate logic. Topics selected from Horn logic, equational logic, resolution and unification, foundations of logic programming, reasoning about programs, program specification and verification, model checking and binary decision diagrams, temporal logic and modal logic.

(Cross-listed with COM S, CPR E). (2-2) Cr. 3. F.

Prereq: MATH 265; MATH 207 or MATH 317
UNIX, serial programming for high performance, OpenMP for high performance, shared memory parallelization. Semester project required.

(3-0) Cr. 3. F.

Prereq: MATH 207 or MATH 317
Euclidean geometry. Points, lines, circles, triangles, congruence, similarity, properties invariant under rigid motions. Synthetic, analytic, and axiomatic methods.

(3-0) Cr. 3. S.

Prereq: MATH 435
Continuation of Euclidean geometry with topics from elliptic, projective, or hyperbolic geometry. Emphasis on analytic methods.

(3-0) Cr. 3. Alt. F., offered odd-numbered years.

Prereq: MATH 265 and either MATH 266 or MATH 267
Iteration of maps; classification of periodic points; bifurcation theory; chaos; Julia sets and the Mandelbrot set; fractals and fractal dimension.

(3-0) Cr. 3. S.

Prereq: MATH 265; STAT 101 or 104 or 105 or 201 or 226.
Applications of mathematical methods to problems in finance. Lagrange Multiplier Method, applications to mean-variance portfolio selection and utility maximization, binomial asset pricing model. Binary Martingales, Optional Stopping Theorem, Central Limit Theorem, applications to financial derivative pricing.

(Cross-listed with COM S). (3-0) Cr. 3. S.

Prereq: MATH 265 and either MATH 266 or MATH 267; knowledge of a programming language
First order Euler method, high order Runge-Kutta method, and multistep method for solving ordinary differential equations. Finite difference and finite element methods for solving partial differential equations. Local truncation error, stability, and convergence for finite difference method. Numerical solution space, polynomial approximation, and error estimate for finite element method.

Cr. 1-3. Repeatable, maximum of 9 credits.

Prereq: Permission of instructor.
No more than 9 credits of Math 490 or Math 490H may be counted toward graduation.

Cr. 1-3. Repeatable, maximum of 9 credits.

Prereq: Permission of the instructor.
No more than 9 credits of Math 490 or 490H may be counted toward graduation.

Cr. 2-3.


Writing and presenting a formal mathematics paper. Upon approval by the department, the paper will satisfy the departmental advanced English requirement.

(2-0) Cr. 2. F.S.

Prereq: MATH 317 or MATH 407
Introduction to independent mathematical thought, with emphasis on oral communication of an advanced topic. Seminar content varies.

Cr. arr. Repeatable, maximum of 9 credits.

Prereq: Permission of instructor
Topics of current interest.

(Cross-listed with C I). (3-0) Cr. 3. F.

Prereq: 15 credits in college mathematics. If in a teacher licensure program, concurrent enrollment in C I 426 or C I 526.
Develop an understanding of instructional planning, lesson implementation, and assessment in grades 5-12 mathematics, with a focus on reform-based mathematics, equity, and conceptual understanding.

Courses primarily for graduate students, open to qualified undergraduates:

(3-0) Cr. 3. F.

Prereq: MATH 265 and (MATH 207 or MATH 317)
A development of the real numbers. Study of metric spaces, completeness, compactness, sequences, and continuity of functions. Differentiation and integration of real-valued functions, sequences of functions, limits and convergence, equicontinuity.

(3-0) Cr. 3. S.

Prereq: MATH 414 or MATH 501
Introduction to general topology. Topological spaces, continuous functions, connectedness, compactness. Topics selected from countability and separation axioms, metrization, and complete metric spaces. Topics in algebraic topology.

(3-0) Cr. 3. F.

Prereq: MATH 302
Algebraic systems and their morphisms, with emphasis on groups and rings.

(3-0) Cr. 3. S.

Prereq: MATH 504
Continuation of MATH 504. Algebraic systems and their morphisms, with emphasis on modules and fields.

(Dual-listed with MATH 407). (3-0) Cr. 3. F.

Prereq: MATH 317; or MATH 207 and experience writing proofs
Advanced topics in applied linear algebra including eigenvalues, eigenvalue localization, singular value decomposition, symmetric and Hermitian matrices, nonnegative and stochastic matrices, matrix norms, canonical forms, matrix functions. Applications to mathematical and physical sciences, engineering, and other fields.

(3-0) Cr. 3. F.

Prereq: MATH 317 or MATH 407 or (MATH 207 and one of MATH 301 or MATH 414)
Advanced topics in linear algebra including canonical forms; unitary, normal, Hermitian and positive-definite matrices; variational characterizations of eigenvalues.

(3-0) Cr. 3. S.

Prereq: MATH 414 or MATH 501
Theory of analytic functions, integration, topology of the extended complex plane, singularities and residue theory, maximum principle, conformal mapping, meromorphic functions, argument principle.

(3-0) Cr. 3. F.

Prereq: MATH 414 or MATH 501
Lebesgue measure and Lebesgue integral, one variable differentiation theory, Fubini and Tonelli theorems in R^n, Lp spaces.

(3-0) Cr. 3. S.

Prereq: MATH 515
Metric spaces, topological spaces, compactness, abstract theory of measure and integral, differentiation of measures, Banach spaces.

(3-0) Cr. 3. S.

Prereq: MATH 481 or MATH 561
Finite difference methods for partial differential equations. Methods for elliptic equations; explicit and implicit methods for parabolic and hyperbolic equations; stability, accuracy, and convergence theory, including von Neumann analysis, modified equations, and the Courant-Friedrichs-Lewy condition.

(3-0) Cr. 3. F.

Prereq: MATH 414 or MATH 501
Techniques of classical and functional analysis with applications to differential equations and integral equations. Vector spaces, metric spaces, Hilbert and Banach spaces, Sobolev spaces and other function spaces, contraction mapping theorem, distributions, Fourier series and Fourier transform, linear operators, spectral theory of differential and integral operators, Green's functions and boundary value problems, weak solutions of partial differential equations and variational methods, calculus in Banach spaces and applications.

(3-0) Cr. 3. S.

Prereq: MATH 519
Continuation of MATH 519.

(Cross-listed with COM S, CPR E). (3-0) Cr. 3. S.

Prereq: CPR E 308 or MATH 481; experience in scientific programming; knowledge of FORTRAN or C
Introduction to parallelization techniques and numerical methods for distributed memory high performance computers. A semester project in an area related to each student’s research interests is required.

(Cross-listed with CPR E, INFAS). (3-0) Cr. 3. S.

Prereq: MATH 301 or CPR E 310 or COM S 330
Basic concepts of secure communication, DES and AES, public-key cryptosystems, elliptic curves, hash algorithms, digital signatures, applications. Relevant material on number theory and finite fields.

(Cross-listed with CPR E, INFAS). (3-0) Cr. 3. Alt. S., offered even-numbered years.

Prereq: E E 524 or MATH 317 or MATH 407 or COM S 330
Basic principles of covert communication, steganalysis, and forensic analysis for digital images. Steganographic security and capacity, matrix embedding, blind attacks, image forensic detection and device identification techniques. Related material on coding theory, statistics, image processing, pattern recognition.

(1-0) Cr. 1. SS.

Prereq: Enrollment in the Master of School Mathematics program or professional studies in education
Research studies in mathematics learning and teaching, exemplary practices in mathematics education, and current state and national trends in the mathematics curriculum in grades K-12. Students in MSM take each of 540A, 540B, and 540C. Topics are offered on a 3-year cycle. A. Assessment, equity, and teaching of statistics. Offered SS 2017. B. Geometry and discrete mathematics, and problem solving. Offered SS 2018. C. Teaching of analysis, algebra, and the use of technology. Offered SS 2016.

(1-0) Cr. 1.

Prereq: Enrollment in the Master of School Mathematics program or professional studies in education
Research studies in mathematics learning and teaching, exemplary practices in mathematics education, and current state and national trends in the mathematics curriculum in grades K-12. Topics are offered on a 3-year cycle. Offered SS 2017.

(1-0) Cr. 1.

Prereq: Enrollment in the Master of School Mathematics program or professional studies in education
Research studies in mathematics learning and teaching, exemplary practices in mathematics education, and current state and national trends in the mathematics curriculum in grades K-12. Offered on a 3-year cycle. Offered SS 2018.

(1-0) Cr. 1.

Prereq: Enrollment in the Master of School Mathematics program or professional studies in education
Research studies in mathematics learning and teaching, exemplary practices in mathematics education, and current state and national trends in the mathematics curriculum in grades K-12. Topics are offered on a 3-year cycle. Offered SS 2016.

(4-0) Cr. 4.

Prereq: 3 semesters of calculus and enrollment in the master of school mathematics program
Offered on a 3-year cycle, offered SS. 2016. The fundamental concepts of calculus which are critical to the effective understanding of the material in first year calculus. Emphasis is on a constructivist approach to learning, cooperative groups, problem solving, and use of technology.

(2-2) Cr. 3.

Prereq: 3 semesters in calculus or concurrent enrollment in 545 and enrollment in the master of school mathematics program
Offered on a 3- year cycle, offered SS. 2016. The use of technology in secondary mathematics with an emphasis on the exploration, creation, and implementation of algorithms.

(4-0) Cr. 4.

Prereq: Enrollment in the master of school mathematics program
Offered on a 3-year cycle, offered SS. 2018. Applications of graph theory, game theory, voting theory, recursion, combinatorics, and algebraic structures. Issues in integrating discrete topics into the secondary curriculum. Use of the computer to explore discrete mathematics.

(3-0) Cr. 3.

Prereq: MATH 435 or equivalent and enrollment in the master of school mathematics program
Offered on a 3-year cycle, offered SS. 2018. A study of geometry with emphasis on metrics, the group of isometries, and the group of similarities. Specific spaces studied normally include the Euclidean plane, the 2-sphere, projective 2-space, and hyperbolic geometry. Emphasis on analytical methods. Incorporation of geometry software.

(Cross-listed with STAT). (3-0) Cr. 3. F.

Prereq: STAT 542
Markov chains on discrete spaces in discrete and continuous time (random walks, Poisson processes, birth and death processes) and their long-term behavior. Optional topics may include branching processes, renewal theory, introduction to Brownian motion.

(3-0) Cr. 3. F.

Prereq: MATH 415 or MATH 501
The initial-value problem, existence and uniqueness theorems, continuous dependence on parameters, linear systems, stability and asymptotic behavior of solutions, linearization, dynamical systems, bifurcations, and chaotic behavior.

(3-0) Cr. 3. F.

Prereq: MATH 414 or MATH 501
Approximation theory, including polynomial interpolation, spline interpolation and best approximation; numerical differentiation and integration; numerical methods for ordinary differential equations.

(3-0) Cr. 3. S.

Prereq: MATH 317
Numerical linear algebra including LU factorization, QR factorization, linear least squares, singular value decompositions, eigenvalue problems, and iterative methods for large linear systems.

(3-0) Cr. 3. S.

Prereq: MATH 265 and one of MATH 317, 507, 510
Theory and methods for constrained and unconstrained optimization. Steepest-descent, conjugate gradient, Newton and quasi-Newton, line search and trust-region, first and second order necessary and sufficient conditions, linear, quadratic and general nonlinear programming.

(3-0) Cr. 3. F.

Prereq: MATH 317 or MATH 507 or MATH 510
Algorithms for linear programming, integer and combinatorial optimization. Linear programming, duality theory, simplex algorithm; the solution of the shortest-path, minimum spanning tree, max-flow/min-cut, minimum cost flow, maximum matching, and traveling salesman problems; integer linear programming, branch-and-bound, local and global search algorithms; matroids and greedy algorithms.

(Cross-listed with AER E, E E, M E). (3-0) Cr. 3. F.

Prereq: E E 324 or AER E 331 or MATH 415; and MATH 207
Linear algebra review. Least square method and singular value decomposition. State space modeling of linear continuous-time systems. Solution of linear systems. Controllability and observability. Canonical description of linear equations. Stability of linear systems. State feedback and pole placements. Observer design for linear systems.

(Cross-listed with AER E, E E, M E). (3-0) Cr. 3. S.

Prereq: E E 577
Linear vs nonlinear systems. Phase plane analysis. Bifurcation and center manifold theory. Lyapunov stability. Absolute stability of feedback systems. Input-output stability. Passivity theory and feedback linearization. Nonlinear control design techniques.

Cr. arr. Repeatable.


(0.5-0) Cr. 0.5. F.


Fall semester orientation seminar. Required for graduate students in Mathematics and Applied Mathematics. Topics include teaching at the university level and communication of mathematics. Offered on a satisfactory-fail basis only.

(0.5-0) Cr. 0.5. S.


Spring semester orientation seminar. Required for graduate students in Mathematics and Applied Mathematics. Topics include teaching at the university level and communication of mathematics. Offered on a satisfactory-fail basis only.

Cr. arr. Repeatable.


Courses for graduate students:

(3-0) Cr. 3. Alt. F., offered odd-numbered years.

Prereq: MATH 504
Model theory of propositional and predicate logic, the Soundness Theorem, the Compactness Theorem, the Goedel-Henkin Completeness Theorem, the Incompleteness Theorem, computability theory. As time permits: modal and temporal logic, set theory (the continuum hypothesis). Emphasis on the relationship between `provable' and `true' and the relationship between `computable' and `definable'.

(3-0) Cr. 3. Alt. F., offered even-numbered years.

Prereq: MATH 504
Combinatorial designs and Latin squares. Construction methods including finite fields. Error-correcting codes. Adjacency matrices and algebraic combinatorics.

(3-0) Cr. 3. Alt. S., offered odd-numbered years.

Prereq: MATH 504
Ordered sets and lattices. Generating functions. Moebius inversion and other enumeration methods.

(3-0) Cr. 3. Alt. F., offered odd-numbered years.

Prereq: MATH 314 or MATH 504
Structural theory of graphs. Topics include basic structures (trees, paths and cycles), networks, colorings, connectivity, topological graph theory, Ramsey theory, forbidden graphs and minors, applications.

(3-0) Cr. 3. Alt. S., offered even-numbered years.

Prereq: MATH 607
Study of extremal graph problems and methods. Topics include canonical Ramsey theory, generalizations of Turan’s theorem, Szemeredi's regularity lemma, random graph theory.

(3-0) Cr. 3. Alt. F., offered even-numbered years.

Prereq: MATH 504
First semester of full-year course. Subalgebras, homomorphisms, congruence relations, and direct products. Lattices and closure operators. Varieties and quasivarieties of algebras, free algebras, Birkhoff's theorems, clones, Mal'cev conditions. Advanced topics.

(3-0) Cr. 3. Alt. S., offered odd-numbered years.

Prereq: MATH 615
Continuation of MATH 615.

(3-0) Cr. 3. Alt. F., offered odd-numbered years.

Prereq: MATH 504
Categories and functors and their applications.

(3-0) Cr. 3. Alt. S., offered even-numbered years.

Prereq: MATH 504
Representations of algebraic structures. Content varies by semester.

(3-0) Cr. 3. Alt. S., offered odd-numbered years.

Prereq: MATH 501 or MATH 515
Topics selected from: Geometry of curves and surfaces. Manifolds, coordinate systems. Tangent and cotangent vectors, vector fields. Tensors, differential forms, Riemannian metrics. Connections, covariant differentiation, curvature tensors. Applications to physics and engineering.

(3-0) Cr. 3. Alt. F., offered odd-numbered years.

Prereq: MATH 515
Fundamental theory of normed linear spaces and algebras, such as topology and continuity, duality and spectral theory, emphasizing aspects that provide a framework for the study of the spectrum of an operator, analytic function theory, and modern operator theory.

(Cross-listed with STAT). (3-0) Cr. 3. F.

Prereq: MATH 414 or MATH 501 or equivalent course.
Sequences and set theory; Lebesgue measure, measurable functions. Absolute continuity of functions, integrability and the fundamental theorem of Lebesgue integration. General measure spaces, probability measure, extension theorem and construction of Lebesgue-Stieljes measures on Euclidean spaces. Measurable transformations and random variables, induced measures and probability distributions. General integration and expectation, Lp-spaces and integral inequalities. Uniform integrability and absolute continuity of measures. Probability densities and the Radon-Nikodym theorem. Product spaces and Fubini-Tonelli theorems.

(Cross-listed with STAT). (3-0) Cr. 3. S.

Prereq: STAT 641, or STAT 543 and MATH 515.
Probability spaces and random variables. Kolmogorov's consistency theorem. Independence, Borel-Cantelli lemmas and Kolmogorov's 0 - 1 Law. Comparing types of convergence for random variables. Sums of independent random variables, empirical distributions, weak and strong laws of large numbers. Convergence in distribution and its characterizations, tightness, characteristic functions, central limit theorems and Lindeberg-Feller conditions. Conditional probability and expectation. Discrete parameter martingales and their properties and applications.

(Cross-listed with STAT). (3-0) Cr. 3. S.


Weak convergence. Random walks and Brownian motion. Martingales. Stochastic integration and Ito's Formula. Stochastic differential equations and applications.

(Cross-listed with PHYS). (3-0) Cr. 3. S.


Modeling of the dynamics of complex systems on multiple scales: Classical and dissipative molecular dynamics, stochastic modeling and Monte-Carlo simulation; coarse grained nonlinear dynamics, interface propagation and spatial pattern formation.

(3-0) Cr. 3. F.

Prereq: MATH 515 or MATH 519
Study of model problems of elliptic, parabolic and hyperbolic types, first order equations, conservation laws, transform methods, introduction to linear partial differential equations of arbitrary order, fundamental solutions.

(3-0) Cr. 3. S.

Prereq: MATH 655
Sobolev spaces, general theory of second order linear elliptic, parabolic and hyperbolic partial differential equations, first order linear hyperbolic systems, variational methods, fixed point methods.

(3-0) Cr. 3. Alt. F., offered even-numbered years.

Prereq: MATH 516 or MATH 520 or MATH 561 or MATH 656
Weak and variational formulations of elliptic problems; weak derivatives and Sobolev spaces; Lax-Milgram theorem, Bramble-Hilbert lemma; examples of finite element spaces; polynomial approximation theory; error estimates for finite element methods; implementation issues; mixed finite element methods for Stokes problems; applications.

Cr. 3. Repeatable.


Cr. arr. Repeatable.