Mathematics
Information
Information
K.L.D. Gunawardena, Chairperson
Department Office: Swart 115
Department Telephone: (920) 4241333
Code 67 or MATH
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Faculty
Faculty
Beam 
Kuennen

Belnap 
Moghadam

Benzaid

Moussavi

Bullington

Muthuvel

Edwards

Parrott

Eroh

Penniston

Ganapathy

Price

Gunawardena

Szydlik J.

Hart

Szydlik S.

Kazmi

Winters

Koker

Zhang



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Degrees
Degrees

Undergraduate: A major in Mathematics can lead to the degree(s): Bachelor of Arts; Bachelor of Science; Bachelor of Science in Education.

Graduate: Students who complete a major in the Mathematics Department may want to continue in our graduate program leading to the degree: Master of Science in Mathematics Education. For specifics, please see the University of Wisconsin Oshkosh Graduate Bulletin.
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Summary of Fields of Study
Summary of Fields of Study
1. Goal(s)
Mathematics is the human expression of pattern and regularity in the world. It involves the study of structures and relationships among ideal objects, including numbers, shapes, functions, and data. Logical reasoning and problem solving are the backbone of mathematics. The mathematics department is committed to empowering students to develop mathematical reasoning and to understand and appreciate the structure and beauty of the discipline.
The department has identified six general goals for students who complete the core mathematics courses of the major:
Communication: Students will be able to read, write, listen and speak mathematically. They will contribute effectively to group efforts; communicate mathematics clearly in ways appropriate to career goals; and make oral and written presentations on various topics. Students will possess skill in expository mathematical writing and have a disposition for questioning. They will be able to listen and engage in mathematical discourse.
Content: Students will be able to demonstrate that they understand the theory and applications of calculus, the basic techniques of linear and abstract mathematics and the basic concepts associated with probability and statistics. They will be prepared to begin a study of higherlevel mathematics.
Connections: Students will possess an understanding of the breadth of the mathematical sciences and their interconnecting principles. They will witness the interplay among applications, problemsolving and theory. They will understand and appreciate connections between different areas of mathematics and with other disciplines and gain awareness of the abstract nature of theoretical mathematics. They will understand the dichotomy of mathematics as an object of study and a tool for application. They will understand the role of technology in the study of mathematics.
Independent Learning/Reading: Students will be able to undertake independent work and will be able to develop ideas and discover mathematics that is new to them. Students should possess an advanced level of critical sophistication; knowledge and skills needed for further study; personal motivation and enthusiasm for studying and applying mathematics; and attitudes of mind and analytical skills required for efficient use, appreciation, and understanding of mathematics.
Problem Solving: Students will be able to perform complex tasks, explore subtly and discern patterns. They will be able to formulate conjectures based on observation and experimentation. They will use appropriate technology to explore mathematics and will recognize the limitations of technology. They will apply mathematics to a broad spectrum of complex problems and issues and will be able to simplify and nonmathematical problem of making reasonable assumptions and then interpret mathematically.
Reasoning/Validation: They will locate, analyze, synthesize and evaluate information; create and document algorithms and undertake intellectually demanding mathematical reasoning. They will demonstrate proficiency to reason rigorously in mathematical arguments.
2. The Major(s)
 The Department offers a Mathematics Major and two emphases: 1) Statistics, and 2) Secondary Education.
3. The Minor(s)

The Department offers five minor(s): 1) Mathematics, 2) Operations Research, 3) Mathematics for Secondary Licensure, 4) Mathematics for Elementary and Middle School Licensure, and 5) Statistics.
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Admission/Graduation Requirements
Admission/Graduation Requirements

To be eligible for graduation students must meet all requirements for the degree being sought in addition to earning a minimum grade point average of 2.00 in all courses required for the Mathematics major or minor. Refer to the following Sections for complete major/minor course requirements.

Those students seeking Wisconsin teacher certification must earn a minimum grade point average of 2.75 in all courses required for their majors and minors in order to meet requirements of the College of Education and Human Services. (Subject to change by COEHS and DPI).
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Required Core Courses
Required Core Courses

Comment:
Students interested in a Mathematics Program should consult the student handbook available online at http://www.uwosh.edu/departments/mathematics.

Core Mathematics Courses:

Mathematics 171 Calculus I 4 cr.

Mathematics 172 Calculus II 4 cr.

Mathematics 222 Introduction to Abstract Mathematics 3 cr.

Mathematics 256 Introduction to Linear Mathematics 3 cr.

Mathematics 273 Calculus III 4 cr.

Mathematics 301 Introduction to Probability and Statistics 3 cr.
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The Major(s), with Emphases and/or Options
The Major(s), with Emphases and/or Options
Mathematics Major
Recommended for students who want to seek a career in a wide variety of fields that value mathematics and mathematical thinking, such as mathematician, statistician, actuary, financial analyst, software developer and teacher. The mathematics major introduces students to a broad range of mathematics disciplines, including analysis, abstract algebra, applied mathematics, probability and statistics. The mathematics major allows students flexibility in choosing their upperlevel courses to suit their interests and career goals. For example, students interested in modeling or computing may wish to focus their elective choices on Applied Mathematics, while those planning to pursue graduate study in mathematics should take a broad range of courses, in consultation with their advisor. The major also offers optional emphases in Statistics and Secondary Education.

Required Units (crs.): 40 minimum

Required Courses: In addition to the core courses:

Analysis Requirement: Choose one course (3 crs): Math 467 or 480

Algebra Requirement: Choose one course (3 crs): Math 346, 347, 348 or 349

Capstone Requirement (23 crs):
The capstone experience will depend on the interests and needs of the student. Students seeking the Secondary Education emphasis are required to complete Math 495 or Math 430. Students seeking the Statistics emphasis are required to complete Math 403 or do a statistics project as part of Math 446 or Math 474. Those preparing for graduate school in mathematics are recommended to complete a research project in mathematics, as part of an independent study or honor's thesis. 
Electives: Sufficient courses from the Department's Upper Level Course List to reach the required minimum number of credits. Courses taken to satisfy the analysis, algebra or capstone requirements above may not be counted as electives. The choice of electives depends on whether the student is seeking an emphasis.
Students not seeking either the Statistics Emphasis or the Secondary Education Emphasis must select at least one course from the Applied category in the Upper Level Course List.Upper Level Course List:
 Algebra: Mathematics 346, 347, 348, 349
 Analysis: Mathematics 375, 467, 480
 Applied: Mathematics 352, 355, 356, 371, 376
 Geometry: Mathematics 331, 334
 Statistics: Mathematics 302, 304, 305, 381, 385, 386, 401
1. Statistics Emphasis
Recommended for students who have a particular interest in a career in statistics, within diverse fields such as agriculture and environmental sciences, business and economics, social sciences, and health sciences.

Required Units (crs.): 40 minimum

Required courses: In addition to the major requirements:

Mathematics: Mathematics 385, 401

Mathematics: Mathematics 403 or 446 or 474

Mathematics: Mathematics 302 or 386

Mathematics: One course from the following: Mathematics 302*, 304, 305, 346, 347, 348, 349, 352, 355, 356, 371, 375, 376, 381, 386*, 467, 480 (*only if not used in requirement above.)

2. Secondary Education Emphasis
Recommended for students who plan to teach mathematics in middle or high school. The mathematics major with a Secondary Education emphasis combines with a program of studies in the College of Education and Human Services and leads to Wisconsin Certification to teach mathematics in secondary schools (grades 512).

Required Units (crs.): 40 minimum

Required Courses: In addition to the major requirements:

Mathematics: Mathematics 295, 331, 334, 495 or 430

One additional mathematics course from any category in the Upper Level Course List

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The Minor(s)
The Minor(s)
1. Mathematics Minor

Required Units (crs.): 24 minimum

Required Courses:

Mathematics: Core Mathematics Courses


Electives: Selected from the mathematics department's Upper Level Course List to meet the minimum unit (credit) requirement.
2. Operations Research Minor
Recommended for students who are majoring in Business, Computer Science, Physical Sciences or similar fields.

Required Units (crs.): 26 minimum

Required Courses:

Mathematics: Mathematics 171, 172, 222, 256 and 301.

Business: Business 341

Supply Chain Management: SCM 342 and 460


Comment: Math 106 and 206 together may be substituted for Math 171 with consent of the mathematics department chair.
3. Mathematics Minor For Secondary Licensure
Recommended for students who are earning a degree in Secondary Education and are planning to teach mathematics or a related field.

Required Units (crs.): 24 minimum

Required Courses:

Mathematics: Mathematics 171, 172, 222, 256, 295, 301, 331.


Electives: Selected from the mathematics department's Upper Level Course List or Mathematics 495 to meet the minimum credit requirement.
4. Mathematics Minor For Elementary and Middle School Licensure
Recommended for students who are earning a degree in Elementary Education, and are interested in teaching Elementary or Middle School Mathematics (Early Childhood through Middle School, or Middle Childhood through Early Adolescence certification).

Required Units (crs.): 24 minimum

Required Courses:

Mathematics: Mathematics 110, 211, 217, 490; plus three courses from: Mathematics 317, 319, 413, and 415.


Comment: Since the upper level courses are not necessarily offered at regularly spaced times, it is important that interested students declare the minor no later than their sophomore year.
5. Statistics Minor
Recommended for students who are in the areas of Business, Computer Science, Education, Mathematics, Natural Science, Physical Science and Social Science.

Required Units (crs.): 26 minimum

Required Courses:

Mathematics: Mathematics 171, 172, 222, 256, 301, and one course from: Mathematics 302, 304, 305, 381, 385, 386.


Electives: Sufficient courses to meet the minimum unit (cr.) requirement selected from the following list:

Business: Business 341

Economics: Economics 472, 473.

Mathematics: Mathematics 302, 304, 305, 381, 385, 386, 401

Supply Chain Management: SCM 342, 460


Comments:
Math 106 and 206 together may be substituted for Math 171 with the consent of the mathematics department chair.
Mathematics majors with an emphasis other than statistics may earn a minor in statistics but they must have a minimum of 52 units (crs.) in Mathematics and Statistics approved by the Statistics adviser.
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Course Offering(s)
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 
ProblemBased Inquiry Seminar 187 
3 (crs.) 
Problem Based Inquiry Seminar (PBIS) (MA)(XM) 

In this course students will develop their problem solving, critical thinking, communications and quantitative skills by exploring a mathematical topic in a problem solving setting. The topic will vary depending on instructor. Students are expected to participate actively in their own learning through class discussions, presentations and group activities and will identify attitudes and beliefs that are conducive to success in problem solving and critical thinking. Students should consult their advisor or the Mathematics Department to determine the topics of individual sections. Successful completion of this course will fulfill the ProblemBased Inquiry Seminar requirement. Prerequisite: Mathematics 103, with grade of C or better or placement. 





ProblemBased Inquiry Seminar 188 
3 (crs.) 
Mathematics and your Political World: Voting, Power, and How You Count (PBIS) (MA)(XM) 

This is a course intended for students whose major program does not require algebra or calculus. Students will see that the connection between the mathematics presented and downtoearth, concrete reallife problems is direct and immediate. Topics are selected from social choice (voting systems, fair division, apportionment), management science (graphs, networks, scheduling), growth and symmetry (growth, populations, patterns), statistics (data analysis, probability, distributions) and computer technology (algorithms, data storage, coding, graphics). Prerequisite: Mathematics 103, with grade of C or better or placement. (FallSpring) 





ProblemBased Inquiry Seminar 189 
3 (crs.) 
Problem Based Inquiry SeminarStatistics (PBIS) (MA)(XM) 

Descriptive statistics/elementary probability/basic problems of statistical inference: estimation, confidence intervals, hypothesis testing, regression and correlation. Prerequisite: Mathematics 103, with grade of C or better or placement. (FallSpring) 




Mathematics 100 
2 (crs.) 
Elementary Algebra I 

The course will focus on basic concepts about real numbers, fundamental operations of arithmetic, algebraic expressions, an introduction to linear equations and problem solving, graphing linear equations, and exponents. Only those students failing to meet the prerequisites for courses at the Mathematics 101 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 101 
2 (crs.) 
Elementary Algebra 2 

The course will focus on basic concepts about problem solving, factoring, 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. Prerequisite: Mathematics 100 with a C or better or placement. 





Mathematics 103 
3 (crs.) 
Intermediate Algebra 

Functions, tables and graphs, problem solving, inequalities in one variable, exponents and radicals, quadratic functions and exponential functions. This course does not count towards the 120 units (crs.) necessary for graduation. Prerequisites: Mathematics 101 with a C or better or placement. Not open to students who have completed Mathematics 104 or higher. (FallSpring) 





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 (XM)(MA) 

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. (FallSpring) 





Mathematics 108 
5 (crs.) 
PreCalculus (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 includes derivatives, antiderivatives, and, if time permits, definite integrals. Applications of differentiation, such as related rates, optimization, and curvesketching, are also covered. A graphic programmable calculator is required. Prerequisites: Mathematics 108 or 104 and 106 with grade(s) of C or better or 4 years of college preparatory mathematics and a satisfactory score on a placement examination. (FallSpring) 





Mathematics 172 
4 (crs.) 
Calculus II (MA) (XM) 

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. (FallSpring) 





Mathematics 175 
4 (crs.) 
Honors: Calculus I (XM)(MA) 

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: PBIS 187, 188 or 189 or Mathematics 104, 108 or 204 with a grade of C or better. (FallSpring) 





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. (FallSpring) 





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. (FallSpring) 





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 K8 guidelines. Prerequisite: Mathematics 110 with a grade of C or better. (FallSpring) 





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. (FallSpring) 





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 TI85 or equivalent technology. Prerequisite: Mathematics 172 with a grade of C or better. (FallSpring) 





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. (FallSpring) 





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 295 
3 (crs.) 
Secondary Mathematics from an Advanced Perspective I 

A deep study of the mathematics required for teaching secondary school mathematics, from a problem solving perspective. Explicit connections will be made with the completed coursework from the mathematics core. The content will be focused on number systems and algebraic properties of the integers, algebra and trigonometry, analytic geometry, and probability and statistics. Prerequisites: Completion of Math 222 with a grade of C or better, and completion of or concurrent registration in Math 301. 





Mathematics 301 
3 (crs.) 
Introduction to Probability and Statistics (MA) (XM) 

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. (FallSpring) 





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 Ksample 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 Elementary and Middle School 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 nonEuclidean 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 prooforiented, 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 singlefactor 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 

A mathematical treatment of advanced statistical methods, beginning with probability. Discrete and continuous, univariate, and multivariate distributions; functions of random variables and moment generating functions, transformations, the theory of estimation and hypothesis testing. Prerequisites: Mathematics 273 and 301 with a grade of C or better. 401/601 (Fall) 





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 glidereflections), 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 9 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 prooforiented, 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: The Honors College 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 nonroutine mathematical problems. Interactive problem solving and analysis by participants. Designed for communicators of mathematics. Prerequisite: Completion of core, Mathematics 222 and 9 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. 





Mathematics 495 
3 (crs.) 
Secondary Mathematics from an Advanced Perspective II 

A deep study of the mathematics required for teaching secondary school mathematics, from a problem solving perspective. Explicit connections will be made with the completed coursework, especially in the upper level geometry, analysis, and algebra courses. Prerequisites: Completion of Core, Math 295, Math 331 and 334, an upper level analysis course (Math 467 or 480), and an upper level algebra course (Math 346, 347 348, or 349). 
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