## Course Offering(s)

**NOTE: Prerequisite courses must be completed with a grade of "C" or better. The Mathematics Department recommendation for students entering their first course in mathematics is made on the basis of the student's high school record, ACT score, University objectives and mathematics placement exam.**

*Students whose first mathematics course at UW Oshkosh is Mathematics 172 Calculus II and who have not received credit for Mathematics 171 Calculus I, may receive retroactive credit for Mathematics 171 under the following conditions:*

*Students must receive permission from the chair of the Math Department to register for Mathematics 172. The chair will take into account the student’s Math ACT score and evidence that the student is properly prepared for Mathematics 172.**Students must earn a grade of C or better in Mathematics 172.**The student must request in writing to the chair of the Math Department that retroactive credit be granted.*

**If you have completed a Math course you may not get credit for a lower level math course. See chart below and also check course descriptions for other restrictions.**

Can't earn credit for: | If you have credit for Math: |
---|---|

Math 103 | 104, 106, 108, 171, 172, 175, 212 |

Math 104 | 108, 171, 172, 175 |

Math 106 | 108, 171, 172, 175 |

PBIS 189, Math 109 | 171, 201, 212, 301 |

Math 171 | 175 |

**Mathematics 100** 4 *(crs.)*

**Elementary Algebra**

Basic concepts about real numbers, fundamental operations of arithmetic, algebraic expressions, an introduction to linear equations and problem solving, graphing linear equations, factoring, exponents and polynomials, rational expressions and equations. Only those students failing to meet the prerequisites for courses at the Mathematics 103 level will be recommended for this course. This course does not count toward the 120 units (crs.) necessary for graduation. A grade of C or better is required to remove mathematics deficiency. (Fall-Spring)

**Mathematics 103** 3 *(crs.)*

**Intermediate Algebra**

Functions, tables and graphs, problem solving, inequalities in one variable, exponents and radicals, quadratic functions, exponential and logarithmic functions. This course does not count towards the 120 units credits (crs.) necessary for graduation. Prerequisites: Mathematics 100 with a C or better or placement. Not open to students who have completed Mathematics 104 or higher. (Fall-Spring)

**Mathematics 104** 3 *(crs.)*

**College Algebra (MA)(XM)**

Equations and inequalities; graphs, functions and models; polynomial and rational functions; exponential and logarithmic functions. May not receive credit for both Mathematics 104 and 108. Prerequisite: Mathematics 103 with grade of C or better or placement.

**Mathematics 106** 2 *(crs.)*

**Trigonometry (MA)(XM)**

A first course in trigonometry. Basic circular functions and their inverses. Trigonometric identities and equations. Triangle trigonometry. Law of Sines and Law of Cosines. Students may not receive credit for both Mathematics 108 and 106. Prerequisite: Mathematics 104 with a grade of C or better or placement. (Fall-Spring)

**Mathematics 108** 5 *(crs.)*

**Pre-Calculus (MA)(XM)**

A functional approach to college algebra and trigonometry. Polynomial, exponential, logarithmic, circular and trigonometric functions. Recommended for all students who place at this level and who expect to take the Mathematics 171 - Mathematics 172 calculus sequence. May not receive credit for both Mathematics 104 and 108. Prerequisite: Mathematics 103 with a grade of C or better or placement.

**Mathematics 109** 3 *(crs.)*

**Elementary Statistics (MA)(XM)**

Descriptive statistics, elementary probability theory, sampling distributions, basic problems of statistical inference including estimation and confidence intervals, tests of hypothesis and regression. Prerequisites: Mathematics 103 with a grade of C or better or placement.

**Mathematics 110** 3 *(crs.)*

**Number Systems**

Exploring, conjecturing, communicating and reasoning within the content domain of the whole numbers, the integers, the rational numbers and the real numbers. Includes experiences with sets, number sense and numeration, number systems, number theory, concepts of operations on numbers, computational algorithms and estimation. Open only to students in Elementary and Special Education. Prerequisite: Math 103, with a grade of C or better or placement.

**Mathematics 171** 4 *(crs.)*

**Calculus I (MA)(XM)**

Calculus I is based on the study of real valued functions of a single variable. The course topic include derivatives, antiderivatives, and, if time permits, definite integrals. Applications of differentiation, such as related rates, optimization and curve-sketching, are also covered. A graphic programmable calculator is required. Prerequisites: Mathematics 108 or 104 and 106 with grade(s) of C or better or four years of college preparatory mathematics and a satisfactory score on a placement examination. (Fall-Spring)

**Mathematics 172** 4 *(crs.)*

**Calculus II**

Definite integration and applications, several techniques of integration, approximation and improper integrals. Numerical differential equations, slope fields, Euler's method, and mathematical modeling. Taylor and Fourier Series. A graphics programmable calculator is required. Prerequisite: Mathematics 171 with a grade of C or better. (Fall-Spring)

**Mathematics 175** 4 *(crs.)*

**Honors: Calculus I (MA)(XM)**

Covers the same subject matter as Mathematics 171 but with greater mathematical depth and emphasis on heuristic problem solving processes, computer or calculator graphics and applications. Prerequisite: University Honors status in addition to the prerequisites for Mathematics 171.

**Mathematics 201** 3 *(crs.)*

**Applied Statistics (MA)(XM)**

An introduction to applied statistics using a statistical computing package such as MINITAB. Topics include: Descriptive statistics, elementary probability, discrete and continuous distributions, interval and point estimation, hypothesis testing, regression and correlation. Prerequisite: Mathematics 104 or 108 with a grade of C or better. (Fall-Spring)

**Mathematics 204** 4 *(crs.)*

**Finite Math for Business (MA)(XM)**

This course is designed to acquaint business students with mathematical techniques which are useful in business and management. Topics include operations on rational expressions, exponents, functions and graphs, systems of equations, linear programming, probability and mathematics of finance. Prerequisites: Mathematics 103 or 104 or 108 with a grade of C or better or placement. (Fall-Spring)

**Mathematics 206** 4 *(crs.)*

**Applied Calculus for Business (MA)(XM)**

Topics include logarithmic and exponential functions, differential and integral calculus and their application to business problems. Prerequisites: Mathematics 104 or 108 or 204 with a grade of C or better or placement. (Fall-Spring)

**Mathematics 211** 3 *(crs.)*

**Fundamentals of Geometry and Measurement for Elementary and Special Education Programs (MA)(XM)**

Intuitive geometry and topology. Introduction to motion geometry. Measurement of length, area, volume and angle size. Includes a content foundation for teaching the geometry and measurement concepts recommended in the DPI K-8 guidelines. Prerequisite: Mathematics 110 with a grade of C or better. (Fall-Spring)

**Mathematics 212** 3 *(crs.)*

**Mathematics for Computer Science**

Required of all Computer Science majors and minors. An introduction to truth tables and boolean functions, set theory, counting principles and the use of permutations and combinations, recurrence relations and the mathematical analysis of algorithms. Topics in discrete probability including random variables and expected values are also discussed. Prerequisites: Mathematics 171 or 206, or placement, and Computer Science 221 with a grade of C or better.

**Mathematics 217** 3 *(crs.)*

**Data Exploration and Analysis**

This course uses activities and experiments to develop ideas about analyzing and reporting data, statistical techniques, probability and simulation. Most activities will involve data gathered from real life situations. Prerequisite: Mathematics 110 with a grade of C or better. (Fall-Spring)

**Mathematics 222** 3 *(crs.)*

**Introduction to Abstract Mathematics**

Basic properties of functions, sets and relations presented in various contexts. Emphasis on the precise use of language, the logical structure of mathematical statements and the structure of proofs. Proof methods include induction, proof by contradiction, direct proof and the construction of examples and counter examples. Examples may be drawn from various topics such as the integers, rational and real numbers, geometry, calculus, combinatorics, modern algebra and real analysis. Prerequisite: Mathematics 172 with a grade of C or better.

**Mathematics 256** 3 *(crs.)*

**Introduction to Linear Mathematics**

An introduction to linear algebra based on the study of matrices, with an emphasis on situations which can be interpreted geometrically in the plane or in space. Topics include: matrix operations, systems of linear equations, determinants, eigenevectors and eigenvalues, properties of Rn with emphasis on R2 and R3 and applications of each of these topics. Most computation will be done on TI-85 or equivalent technology. Prerequisite: Mathematics 172 with a grade of C or better. (Fall-Spring)

**Mathematics 273** 4 *(crs.)*

**Calculus III**

Vectors in two and three dimensions and vector functions. Multivariate differential and integral calculus, partial derivatives and multiple integrals. Line and surface integrals. Prerequisite: Mathematics 172 with a grade of C or better. (Fall-Spring)

**Mathematics 287** 1 *(crs.)*

**Elementary Topics in Mathematics**

Elementary level topics from such areas as: decision theory, game theory, graphs and networks, linear programming, applications of calculus to biology, ecology and the social sciences, mathematical modeling, and statistics. Prerequisite: Mathematics 104 or 108 with a grade of C of better.

**Mathematics 301** 3 *(crs.)*

**Introduction to Probability and Statistics**

Elementary probability models, discrete and continuous random variables, sampling and sampling distributions, estimation, and hypothesis testing. Prerequisite: Mathematics 172 with a grade of C or better. (Fall-Spring)

**Mathematics 302** 3 *(crs.)*

**Intermediate Statistical Methods**

Emphasis on models and methods used in statistical applications. Topics covered include: two sample procedures, linear regression and correlation, analysis of variance and distribution free procedures. Prerequisites: Mathematics 201 or 301 with a grade of C or better.

**Mathematics 304** 3 *(crs.)*

**Introduction to Nonparametric Methods**

Statistical methods when the functional form of the population is unknown. Emphasis on applications and comparison of methods. One and two sample tests, contingency tables, tolerance limits, confidence intervals for means, tests of significance for some measures of correlation and K-sample tests. Prerequisite: Mathematics 201 or 301 with a grade of C or better.

**Mathematics 305** 3 *(crs.)*

**Statistics for Quality and Productivity**

Statistical process control charts including Shewart and CUSUM. Design of experiments including factorials, fractional factorials and designs to explore response surfaces. The roles of blocking, confounding and randomization. The course will be about 25% statistical process control and about 75% design of experiments. Prerequisite: Mathematics 301 with a grade of C or better. 305/505

**Mathematics 317** 4 *(crs.)*

**Probability and Statistics for Elementary and Middle School Programs**

An introduction to probability and statistics emphasizing problem solving and communication. Topics include sample spaces, permutations and combinations, random variables, expected value, probability distributions, hypothesis testing and statistical inference. This course will employ technology and contain a historical component. Prerequisites: Mathematics 211 and 217 each with a grade of C or better. 317/517

**Mathematics 319** 4 *(crs.)*

**Infinite Processes for Elem & Mid Sch Programs**

An introduction to infinite processes; this course emphasizes problem solving and communication. Topics include functions, continuity, limiting processes, rates of change, optimization, approximation of areas and volumes, sequences and series. This course will employ technology and will contain a historical component. (May not receive credit for both Mathematics 319 and Mathematics 171.) Prerequisites: Mathematics 211 and 217 each with a grade of C or better.

**Mathematics 331** 2 *(crs.)*

**Fundamentals of Geometry**

An introduction to the evolution of geometry, modern elementary geometry, transformation theory and modern axiomatic Euclidean geometry. Prerequisite: Mathematics 222. (Spring)

**Mathematics 333** 2 *(crs.)*

**Synthetic Projective Geometry**

Topics include duality, harmonic sequences, projective transformations and conics. Prerequisite: Mathematics 331 with a grade of C or better.

**Mathematics 334** 2 *(crs.)*

**Hyperbolic Geometry**

This course will survey the history of non-Euclidean geometry and develop the basic properties of hyperbolic geometry. A consistency model will be constructed in the Euclidean plane and hyperbolic trigonometry developed by the use of this model. Prerequisite: Mathematics 331 with a grade of C or better. (Spring)

**Mathematics 346** 3 *(crs.)*

**Linear Algebra**

This course is a proof-oriented, abstract approach to the study of finite dimensional vector spaces and linear transformations. Linear Algebra is central in mathematics and used heavily in other areas, such as computer science, economics and physics. Topics include bases and dimension, matrices, determinants, inner product spaces and characteristic values and characteristic vectors. Additional topics may include the Jordan canonical form, the spectral theorem, and quadratic forms. Prerequisite: Math 222 and Math 256 each with a grade of C or better. 346/546 (Fall)

**Mathematics 347** 3 *(crs.)*

**Introduction to Group Theory**

A group is an algebraic system described by a set equipped with one associative operation. Groups contain an identity element and every element has an inverse. Group theory has applications in diverse areas such as art, biology, geometry, linguistics, music and physics. The kinds of groups covered in this class include permutation, symmetric, alternating and dihedral groups. Some of the important theorems covered are Cayley's Theorem, Fermat's Little Theorem, Lagrange's Theorem and the Fundamental Theorem of Finite Abelian Groups. Prerequisite: Math 222 with a grade of C or better. 347/547

**Mathematics 348** 3 *(crs.)*

**Introduction to Ring Theory**

A ring is an algebraic system described by a set equipped with addition and multiplication operations. Rings arise naturally as generalized number systems. The integers, for example, form a ring with the usual addition and multiplication operations. Ring theory has applications in diverse areas such as biology, combinatorics, computer science, physics and topology. Topics include rings of matrices, integers modulo n, polynomials and integral domains. Some of the important theorems covered are the Fundamental Theorem of Algebra, the Division and Euclidean Algorithms, and Eisenstein's Criterion. Prerequisite: Math 222 with a grade of C or better. 348/548

**Mathematics 349** 3 *(crs.)*

**Introduction to Number Theory**

Number Theory is a branch of mathematics that involves the study of properties of the integers. Topics covered include factorization, prime numbers, continued fractions and congruencies as well as more sophisticated tools such as quadratic reciprocity, Diophantine equations, and number theoretic functions. However, many results and open questions in number theory can be understood by those without an extensive background in mathematics. Additional topics might include Fermat's Last Theorem, twin primes, Fibonacci numbers, and perfect numbers. Prerequisite: Math 222 with a grade of C or better. 349/549

**Mathematics 352** 3 *(crs.)*

**Computing Mathematics with Applications**

An introduction to a Computer Algebra System such as Maple, Mathematica or Matlab. The course begins by exploring the symbolic, numerical and graphical capabilities of the software. Topics include lists, sets, arrays, functions and some programming with applications to algebra, calculus, discrete mathematics, linear mathematics, differential equations, probability and statistics and number theory. Students will work in groups and will complete projects exploring some mathematical problems using the software. Prerequisite: Mathematics 172.

**Mathematics 355** 3 *(crs.)*

**Introduction to Numerical Analysis**

Topics in numerical computations selected from polynomial interpolation, solution of nonlinear equations, numerical integration, numerical solution of differential equations and approximation. Prerequisite: Mathematics 273 and Computer Science 221 or equivalent each with a grade of C or better. 355/555

**Mathematics 356** 3 *(crs.)*

**Linear Numerical Analysis**

Topics in numerical linear algebra selected from: Gaussian elimination, matrix inversion, eigenvector and eigenvalue computations, error analysis, condition numbers and pivoting strategies. Prerequisite: Mathematics 256, 273 and Computer Science 221 or equivalent each with a grade of C or better. 356/556

**Mathematics 357** 3 *(crs.)*

**Linear Programming**

Application and theory of linear programming. Primal and dual formulations, sensitivity analysis, simplex method, transportation algorithm and the assignment problem. Students will learn modeling and how to apply linear programming to problems. Case studies are used. This course is appropriate for mathematics students as well as students from other fields. Prerequisite: Mathematics 256.

**Mathematics 365** 2 *(crs.)*

**Math Modeling**

Research, analysis and construction of mathematical models for 'real world' problems. Application to areas within and outside mathematics. Oral group presentations and a written technical report are required. Prerequisite: Completion of core plus 12 units (crs.) in math numbered 300 or above. (Spring)

**Mathematics 371** 3 *(crs.)*

**Differential Equations**

An introductory course treating ordinary differential equations of the first and second order; linear equations with constant coefficients; solutions using series, the Laplace transform and numerical methods. Prerequisite: Mathematics 172. 371/571 (Spring)

**Mathematics 375** 3 *(crs.)*

**Vector & Complex Analyses**

Topics in mathematics applicable to the physical sciences: Vector analysis, Green's theorem and generalizations, analytic function theory. Prerequisite: Mathematics 273. 375/575

**Mathematics 376** 3 *(crs.)*

**Partial Differential Equations and Boundary Value Problems**

Topics in mathematics applicable to the physical sciences: solutions of certain classical differential equations (ordinary and partial), Fourier methods and applied linear algebra. Prerequisite: Mathematics 371. 376/576

**Mathematics 381** 3 *(crs.)*

**Stochastic Modeling**

Conditional probability and conditional expectation, Markov chains, Poisson processes, branching processes and population growth. Prerequisite: Mathematics 256, Math 273 and Math 201 or Math 301 all with grades of C or better. 381/581

**Mathematics 385** 3 *(crs.)*

**Applied Regression Analysis**

A practical introduction to regression emphasizing applications rather than theory. Simple and multiple regression analysis, basic components of experimental design and elementary model building. Both conventional and computer techniques will be used in performing the analyses. Prerequisite: Mathematics 256 and 201 or Math 301 each with a grade of C or better. 385/585

**Mathematics 386** 3 *(crs.)*

**Linear Statistical Models**

A unified approach to the application of linear statistical models in analysis of variance (ANOVA) and experimental design. In ANOVA topics from single-factor ANOVA and multifactor ANOVA will be considered. Experimental design will include randomized blocks, Latin squares and incomplete block designs. Prerequisite: Mathematics 256 and 201 or Math 301 each with a grade of C or better. 386/586

**Mathematics 401** 3 *(crs.)*

**Mathematical Statistics I**

Probability and combinatorial methods. Discrete and continuous, univariate and multivariate distributions, expected values, moments, normal distributions and derived distributions. Prerequisite: Mathematics 273 and 201 or Math 301 each with a grade of C or better. 401/601 (Fall)

**Mathematics 402** 3 *(crs.)*

**Mathematical Statistics II**

Estimation, testing hypothesis, analysis of variance, comparison of means, least squares analysis, regression and correlation. Prerequisite: Mathematics 401. 402/602 (Spring)

**Mathematics 403** 2 *(crs.)*

**Issues in Statistical Practice**

Selected readings and projects illustrating some of the special problems encountered by professional statisticians in their roles as consultants, educators and researchers. Prerequisite: Mathematics 401 and at least two courses from Mathematics 303, 305, 381, 385 and 386. (Spring)

**Mathematics 413** 4 *(crs.)*

**Modern Algebra for Elementary and Middle School Programs**

An intuitive and investigative study of selected mathematical structures (groups, rings, integral domains, fields and vector spaces), sets, operations and functions including historical aspects. Emphasis is on problem solving. Prerequisites: Mathematics 211 and 217 each with a grade of C or better. 413/613

**Mathematics 415** 4 *(crs.)*

**Modern Geometry for Elementary and Middle School Programs**

An informal approach to geometry. Topics are chosen from transformational (motion) geometry (reflections, rotations, translations and glide-reflections), symmetry, fractal geometry, spatial visualization, topology and graph theory including historical aspects. Emphasis is on problem solving and reasoning using technology and math manipulatives. The course will contain a historical component. Prerequisites: Mathematics 211 and 217 each with a grade of C or better. 415/615

**Mathematics 430** 3 *(crs.)*

**International Comparative Mathematics Education Seminar**

Survey and study of research literature on comparative mathematics education, including cultural perceptions on the nature of mathematics and the teaching and learning of mathematics. Analysis of international studies in mathematics achievement. Comparison of standards and curricula for teaching school mathematics. Experience with units from demonstration projects in international primary or secondary school curriculum materials. Prerequisites: Senior status with a major in elementary education and completion of 17 units (crs) toward a minor in mathematics; or completion of core, Mathematics 222 and nine units (crs) in math numbered 300 or above; or consent of instructor.

**Mathematics 446** 1-3 *(crs.)*

**Independent Study**

See Independent Study under Course and Academic Advisement Policies information for general course description, general prerequisites and proper contract form requirements.

**Mathematics 467** 3 *(crs.)*

**Introduction to Real Analysis**

This course offers a proof-oriented, abstract approach to many of the concepts covered in Calculus. Topics include real number properties, the topology of the real numbers, functions, limits of functions, continuity, uniform continuity, differentiation, integration, sequences, series, pointwise and uniform convergence of sequences of functions, and series of functions. Reading and writing proofs are an integral part of the course. Prerequisites: Mathematics 222 and 273. 467/667

**Mathematics 474** 1-6 *(crs.)*

**Honors: Thesis**

Honors thesis projects include any advanced independent endeavor in the student's major field of study: e.g. a written thesis, scientific experiment or research project, or creative arts exhibit or production. Proposals (attached to Independent Study Contract) must show clear promise of honors level work and be approved by a faculty sponsor. Course title for transcript will be 'Honors Thesis'. Completed projects will be announced and presented to interested students and faculty. Prerequisite: University Honors program and junior standing.

**Mathematics 480** 3 *(crs.)*

**Introduction to Topology**

An introduction to the fundamental concepts of point set topology. Topics are chosen from: general topological spaces, functions and continuity, open and closed sets, neighborhoods, homeomorphism, properties of topological spaces, subspaces, products and quotients. Emphasis will be placed on proofs and examples, with particular attention given to metric spaces. Prerequisite: Mathematics 222 and 273. 480/680

**Mathematics 485** 2 *(crs.)*

**Seminar in Mathematical Problem Solving**

General heuristic strategies applied to non-routine mathematical problems. Interactive problem solving and analysis by participants. Designed for communicators of mathematics. Prerequisite: Completion of core, Mathematics 222 and nine units (crs.) in math numbered 300 or above. 485 (Spring)

**Mathematics 490** 3 *(crs.)*

**Senior Seminar for Elementary and Middle School Programs**Seminar emphasizing problem solving and mathematical modeling in Elem/Middle School programs. Survey and study of research literature on the teaching and learning of mathematics, connections between the other courses in the mathematics minor. Experience with units from demonstration projects in middle school curriculum materials. Prerequisite: Senior status with major in elementary education and completion of 17 units (crs.) toward a minor in mathematics.

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