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# University Catalog

### MATH 337. Geometry for K-8 Teachers

Credits: 3
 Description: Geometric concepts, spatial visualization, spatial reasoning, justification, and proof. Techniques, technology, and current trends in the teaching and learning of geometry. Prerequisites: MATH 112, MATH 171 or MATH 211, and MATH 330 Semester Offered: DEMAND

### MATH 353. Operations Research Models

Credits: 3
 Description: Construction and solution of mathematical models associated with operations research. Prerequisites: MATH 222 Semester Offered: Odd Spring

### MATH 411. Modern Algebra I

Credits: 4
 Description: Groups, subgroups, cyclic groups, permutation groups, isomorphisms, Cayley's theorem, cosets, LaGrange's theorem, normal subgroups, quotient groups, homomorphisms, the first isomorphism theorem, construction of the integers and rational numbers from the natural numbers, rings, integral domains, and fields. Prerequisites: MATH 304 and MATH 312, or consent of instructor Semester Offered: Fall

### MATH 412. Modern Algebra II

Credits: 3
 Description: Ideals, factor rings, ring homomorphisms, polynomial rings, factorization of polynomials, irreducible polynomials, Euclidean domains, introduction to fields, extension fields, splitting fields, algebraic and transcendental numbers, geometric construction. Prerequisites: MATH 411 Semester Offered: DEMAND

### MATH 421. Real Analysis I

Credits: 4.0
 Description: The real number system, completeness of the real numbers, topology of the real numbers, sequences, limits, continuity, differentiation, and integration. Prerequisites: MATH 222, MATH 304 Semester Offered: Spring

### MATH 422. Introduction to Real Analysis II

Credits: 3
 Description: Series, power series, uniform and pointwise convergence, Reimann integration, and applications. Prerequisites: MATH 421 Semester Offered: DEMAND

### MATH 423. Complex Variables

Credits: 3
 Description: The complex field, the theory of analytic functions, power series. Fundamental theorem of algebra. Prerequisites: MATH 320 or MATH 321 Semester Offered: Odd Spring

### MATH 427. Partial Differential Equations

Credits: 3
 Description: Partial differential equations of mathematical physics, boundary value problems, classical solution methods, Bessel functions. Prerequisites: MATH 320 or MATH 321, MATH 325 or MATH 327 Semester Offered: Odd Fall

### MATH 428. Introduction to Probability Models

Credits: 3
 Description: Probability theory, random variables, Markov chains, Poisson process, queueing theory. Prerequisites: MATH 222 Semester Offered: DEMAND

### MATH 431. Professional Subject Matter for Middle Grades Mathematics

Credits: 3
 Description: For teacher candidates only. Number sense, patterns and functions, number theory, geometry, data analysis and probability, current curriculum and pedagogical developments, lesson planning, and microteaching. Should be taken within one year prior to student teaching. Prerequisites: Passing scores on the Minnesota Teacher Licensure Examination Basic Skills Tests or instructor permission, and one of MATH 304, MATH 312, MATH 321, or MATH 325 Corequisites: STEM 420, ED 431, IM 422 Semester Offered: Fall

### MATH 432. Professional Subject Matter for Secondary School Mathematics

Credits: 4
 Description: For teacher candidates only. Algebra, geometry, data analysis, and advanced topics; current curriculum and pedagogical developments, lesson planning, and microteaching. Should be taken within one year prior to student teaching. Prerequisites: Passing scores on the Minnesota Teacher Licensure Examination Basic Skills Tests or instructor permission, and one 400-level mathematics course. Corequisites: STEM 421, ED 451, ED 421 Semester Offered: Spring

### MATH 433. Algebra for Elementary and Middle School Teachers

Credits: 3
 Description: Algebraic concepts, representations, structures and applications. Prerequisites: MATH 330 Semester Offered: DEMAND

### MATH 435. Teaching Problem Solving in Elementary School Mathematics

Credits: 3
 Description: Problem solving strategies, teaching problem solving, problem solving via concrete materials, cooperative learning. For elementary education majors only. Prerequisites: MATH 330 Semester Offered: DEMAND

### MATH 439. Using Technology to Teach Science and Mathematics, K-8

Credits: 3
 Description: Demonstrating and exploring technology, such as computers and calculators, that enhances mathematics and science learning and instruction in the K-8 curriculum. Lab activities that involve collecting, representing, and analyzing data. Prerequisites: MATH 330 Semester Offered: DEMAND

### MATH 440. Theoretical Problem Solving

Credits: 1
 Description: Mathematical problem solving, including calculus, differential equations, linear algebra, and proof techniques. Preparation for math competitions. Must be currently enrolled in or have completed 273, 312, 325, or permission of instructor. Semester Offered: DEMAND

### MATH 444. Internship

Credits: 1-16
 Description: Internships are offered at the discretion of departments. Course number and number of credits are determined by the departments. Contact departmental offices for further information. 16 credits maximum in any one program. Semester Offered: FallSpringSummer

### MATH 452. Numerical Analysis

Credits: 3
 Description: Round-off error and computer arithmetic. Solutions of equations in one variable. Interpolation and polynomial approximation. Numerical integration and differentiation. Error Analysis. Prerequisites: MATH 222, MATH 252 or permission of instructor Semester Offered: Even Spring

### MATH 453. Numerical Linear Algebra

Credits: 3
 Description: Direct and iterative solutions in linear algebra. Orthogonal polynomials, splines and least squares approximations. Error analysis. Prerequisites: MATH 222, MATH 312, MATH 252 or CSCI 201 Semester Offered: DEMAND

### MATH 455. Mathematical Modeling

Credits: 3
 Description: Derivation and analysis of mathematical models using differential equations to describe real-world phenomena. Graphical and numerical solution techniques. Nonlinear differential equations and stability. Prerequisites: MATH 327 or (MATH 312 and MATH 325) Semester Offered: Even Fall

### MATH 465. Elements of Geometry

Credits: 3
 Description: Axiomatic systems, foundations of Euclidean geometry, plane Euclidean geometry, and non-Euclidean and transformational geometries. Prerequisites: High school geometry, MATH 304, MATH 312 Semester Offered: Spring

### MATH 480. Topics in Mathematics

Credits: 3
 Description: Designed for intensive study in a special topic in pure or applied mathematics. Topic will be announced in class schedule. Approval of instructor required for enrollment. May be repeated to maximum of 6 credits. Semester Offered: DEMAND

### MATH 482. Student Teaching Seminar

Credits: 2
 Description: For teacher candidates only. Reflections of and extensions of the student teaching experience in a seminar format; individual classroom observations. Must be taken concurrently with student teaching. S/U grading option only. Semester Offered: FallSpring

### MATH 483. Topics in Elementary School Mathematics

Credits: 3
 Description: In depth study of a special topic in mathematics relevant to the elementary school curriculum. Prerequisites: MATH 330 Semester Offered: DEMAND

### MATH 485. Mathematics Seminar

Credits: 2
 Description: Readings, discussion of, and preparation of professional papers in mathematics. Satisfies the upper-division writing requirement (UDWR) for BA mathematics majors. Prerequisites: One 400-level mathematics course. Semester Offered: Fall

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