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Mathematics

 

Information

 

K.L.D. Gunawardena, Chairperson

Department Office: Swart 115
Department Telephone: (920) 424-1333

Code 67 or MATH

 

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
 
 
 

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.
 

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 higher-level 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, problem-solving 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 use reasonable simplifying assumptions to create mathematical models useful in solving quantitative problems.
  • Reasoning/Validation:  Students will locate, analyze, synthesize and evaluate information, create and document algorithms, and undertake intellectually demanding mathematical reasoning. They will demonstrate proficiency in crafting rigorous mathematical arguments.

 

2. The Major(s)

  • The Department offers a Mathematics Major and two emphases: 1) Statistics, and 2) Teaching.

 

3. The Minor(s)

  • The Department offers five minor(s): 1) Mathematics, 2) Operations Research, 3) Mathematics for Teaching, 4) Mathematics for Elementary and Middle School Licensure, and 5) Statistics.
 

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).
 

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.
 

The Major(s), with Emphases and/or Options

 

1. 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 upper-level 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 Teaching.

A. Mathematics

  • Required Credits: 40 minimum
  • Required Courses: In addition to the core courses:
    • Mathematics: Mathematics 273, 301 
    • Analysis Requirement: Choose one course (3 crs): Mathematics 467 or 480
    • Algebra Requirement: Choose one course (3 crs): Mathematics 346, 347, 348 or 349
    • Applied Requirement: Choose one course (3crs): Mathematics 352, 355, 356, 371, 376
    • Capstone Requirement (2-3 crs): Mathematics 365, 403, 430, 446, 474, 495
      The capstone experience will depend on the interests and needs of the student.  Those preparing for graduate school in mathematics are recommended to complete a research project in mathematics, as part of an independent study or honors 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.
      • 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

B. 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 Credits: 40 minimum
  • Required Courses: In addition to the core courses:
    • Mathematics: Mathematics 273, 301
    • Statistics: Mathematics 385, 401
    • Statistics: Mathematics 302 or 386
    • Analysis Requirement: Choose one course (3 crs): Mathematics 467 or 480
    • Algebra Requirement: Choose one course (3 crs): Mathematics 346, 347, 348 or 349
    • 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.)
    • Capstone Requirement (2-3 crs): Mathematics 403 or 446 or 474

C. Teaching Emphasis
Recommended for students who plan to teach mathematics in middle or high school.  The mathematics major with a Teaching 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 5-12).

  • Required Credits: 40 minimum
  • Required Courses: In addition to the core courses:
    • Mathematics: Mathematics 110, 211, 213, 317, 413, 415
    • Abstract Math Requirement: Mathematics 348 or 467
    • Capstone Requirement: (2-3 crs): Mathematics 430 or 432 or 490

The Minor(s)

 

1. Mathematics Minor

Recommended for students who are majoring in fields related to Mathematics such as Business, Computer Science, Economics, Natural Sciences, Physical Sciences.
  • Required Credits: 23 minimum
  • Required Courses:
    • Mathematics: Core Mathematics Courses
    • Mathematics: Mathematics 273, 301
  • Electives: Selected from the mathematics department’s Upper Level Course List to meet the minimum credit requirement.

 

2. Operations Research Minor

Recommended for students who are majoring in Business, Computer Science, Physical Sciences or similar fields.

  • Required Credits: 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 Teaching

Recommended for students who are earning a degree in Secondary Education and are planning to teach mathematics or a related field.

  • Required Credits: 25 minimum
  • Required Courses:
    • Mathematics: Mathematics 110, 171, 172, 213, 222, 413, 415

 

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 Credits: 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 Credits: 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 credit 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 credits in Mathematics and Statistics approved by the Statistics advisor.

 

Course Offerings

Mathematics     81

3 (crs.)

Topics in Geometry

This course will focus on basic concepts of Geometry and real-world objects, as well as to understand the principles of inductive and deductive reasoning. Students will learn to understand common geometric terminology and to recognize geometric shapes. This course study will incorporate the ability to be able to estimate, measure, and deduce measures of length, angles, area, and volume, to understand concepts relating to triangles and quadrilaterals, to learn the Pythagorean Theorem and how to apply it, and to be able to use formulas appropriately for finding perimeter, area, surface area, and volume. Only students who have not taken Geometry in high school will be required to take this course. This course does not count toward the 120 credits necessary for graduation. A grade of D or better is required to remove this mathematics deficiency. (Fall/Spring)

Mathematics     90

2 – 3 (crs.)

Basic Mathematics

Designed for students with minimum algebra background or who have been away from mathematics for several years. Subject areas to be covered include arithmetic of whole numbers, fraction and decimals, ratios and percents, and basic algebraic concepts. Prepares the student for Elementary Algebra. This course does not count toward the 120 units (crs.) necessary for graduation.

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 credits (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. (Fall-Spring)

Mathematics    104

3 (crs.)

College Algebra (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)

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 (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 (XM)

Descriptive statistics, elementary probability theory, sampling distributions, basic problems of statistical inference including estimation and confidence intervals, tests of hypothesis and regression. PR: Math 101 with a grade of C or better or placement.

Mathematics    110

4 (crs.)

Number Systems for Teaching (XM)

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, ratios, proportional reasoning, 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. Special fees may apply.

Mathematics    161

3 (crs.)

Technical Calculus I (XM)

Technical Calculus I course topics include derivatives and antiderivatives with an emphasis on applications to various scientific and technical fields, especially electrical and mechanical engineering. The course includes a scientific computation component in which students will apply mathematical techniques to engineering models using software packages such as Matlab and Maple. Prerequisites: Mathematics 108 or 104 and 106 with grades of C or better or 4 years of college preparatory mathematics and a satisfactory score on a placement examination.

Mathematics    162

3 (crs.)

Technical Calculus II (XM)

Technical Calculus II course topics include definite integration and series using several techniques with an emphasis on applications to various scientific and technical fields, especially electrical and mechanical engineering. The course includes a scientific computation component in which students will apply mathematical techniques to engineering models using software packages such as Matlab and Maple. Prerequisites: Mathematics 161 with a grade of C or better.

Mathematics    171

5 (crs.)

Calculus I (XM)

Calculus I is based on the study of real valued functions of a single variable. The course topics includes limits and continuity, derivatives, antiderivatives, definite integrals and Riemann sums. Applications of differentiation and integration are also covered. Prerequisites: Mathematics 108 or 104 and 106 with grade(s) of C or better or placement. (Fall-Spring) Special fees may apply.

Mathematics    172

4 – 5 (crs.)

Calculus II (XM)

Techniques of integration, improper integrals, elementary differential equations and mathematical modeling, sequences and series, Taylor series, and parametric equations. Prerequisite: Mathematics 171 with a grade of C or better. (Fall-Spring)

Mathematics    175

4 (crs.)

Honors: Calculus I (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    186

3 (crs.)

Problem Based Inquiry Seminar in Quantitative Reasoning (XM)

This course is intended to develop analytic reasoning and the ability to solve quantitative problems. Topics to be covered include construction and interpretation of graphs, functional relationships, descriptive statistics, geometry and spatial visualization, math of finance, exponential growth, and basic probability. Appropriate use of units and dimensions, estimates, mathematical notation and available technology will be emphasized throughout the course. Prerequisites: Math 101 with a grade of C or better or placement. Concurrent enrollment in Math 103 is recommended for students who place into Math 103 and are seeking a Bachelor of Science or a Bachelor of Science in Nursing.

Mathematics    187

3 (crs.)

Problem Based Inquiry Seminar (PBIS) (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.  Prerequisite: Mathematics 101 with grade of C or better or placement. Concurrent enrollment in Math 103 is recommended for students who place into Math 103 and are seeking a Bachelor of Science or a Bachelor of Science in Nursing.

Mathematics    188

3 (crs.)

Problem Based Inquiry Seminar in Mathematics and your Political World (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 down-to-earth, concrete real-life 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 101 with grade of C or better or placement. Concurrent enrollment in Math 103 is recommended for students who place into Math 103 and are seeking a Bachelor of Science or a Bachelor of Science in Nursing. (Fall-Spring)

Mathematics    188Q1

3 (crs.)

Problem Based Inquiry Seminar in Mathematics and your Political World (PBIS) (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 down-to-earth, concrete real-life 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 101 with grade of C or better or placement. Concurrent enrollment in Math 103 is recommended for students who place into Math 103 and are seeking a Bachelor of Science or a Bachelor of Science in Nursing. (Fall-Spring)

Mathematics    189

4 (crs.)

Problem Based Inquiry Seminar in Statistics (MA)(XM)

Descriptive statistics/elementary probability/basic problems of statistical inference: estimation, confidence intervals, hypothesis testing, regression and correlation. Prerequisite: Mathematics 101 with grade of C or better or placement. Concurrent enrollment in Math 103 is recommended for students who place into Math 103 and are seeking a Bachelor of Science or a Bachelor of Science in Nursing. (Fall-Spring)

Mathematics    189Q1

4 (crs.)

Problem Based Inquiry Seminar in Statistics & Citizenship (MA)(XM)

Descriptive statistics/elementary probability/basic problems of statistical inference: estimation, confidence intervals, hypothesis testing, regression and correlation. Prerequisite: Mathematics 101 with grade of C or better or placement. Concurrent enrollment in Math 103 is recommended for students who place into Math 103 and are seeking a Bachelor of Science or a Bachelor of Science in Nursing. (Fall-Spring)

Mathematics    189Q2

4 (crs.)

Problem Based Inquiry Seminar in Statistics & Citizenship (XM)

Descriptive statistics/elementary probability/basic problems of statistical inference: estimation, confidence intervals, hypothesis testing, regression and correlation. Prerequisite: Mathematics 101 with grade of C or better or placement. Concurrent enrollment in Math 103 is recommended for students who place into Math 103 and are seeking a Bachelor of Science or a Bachelor of Science in Nursing. (Fall-Spring)

Mathematics    201

3 (crs.)

Applied Statistics (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: Math 103 with a grade of C or better (or placement above it) and a grade of C or better in Math 104, 108, 110, 186, 187, 188, 189, or placement into Math 201. (Fall-Spring)

Mathematics    204

4 (crs.)

Finite Math for Business (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 (XM)

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

Mathematics    211

2 (crs.)

Geometry and Measurement Teaching (XM)

Exploring, conjecturing, communicating and reasoning within the content domain of geometry. Foundational ideas of geometry including role of definitions, the idea of axioms, and the nature of mathematical objects. Measurement of length, area, volume and angle size. 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    213

2 (crs.)

Transformations, Probability and Data for Teaching

Exploring, conjecturing, communicating and reasoning within the content domains of transformational geometry, probability, and data analysis. This course uses activities and experiments to develop ideas about transformations of the plane including rigid motions and dilations, similarity in 1, 2 and 3 dimensions; analyzing and reporting single variable data; probability, and simulation. Prerequisite: Mathematics 211 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 171 with a grade of C or better. (Fall-Spring)

Mathematics    273

3 – 4 (crs.)

Calculus III

Vectors in two and three dimensions, dot and cross products, lines, and planes. Vector functions and their differentiation and integration. Multivariate differential and integral calculus, partial derivatives and their applications, gradients, and multiple integrals. Line and surface integrals, fundamental theorem of line integrals, Green’s theorem, and Stokes’ theorem. Prerequisite: Mathematics 172 with a grade of C or better. (Fall-Spring) Special fees may apply.

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 (XM)

Elementary probability models, discrete and continuous random variables, sampling and sampling distributions, estimation, and hypothesis testing. Prerequisite: Mathematics 171 with a grade of C or better. (Fall-Spring)

Mathematics    302

3 (crs.)

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 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 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 Teaching

An introduction to probability and statistics emphasizing modeling, problem solving and communication. Topics include fundamental ideas of combinatories (permutations & combinations), probability (sample spaces, theoretical/experimental probabilities, random variables, expected values, and conditional probabilities), descriptive statistics (measures of center & spread), and inferential statistics (correlation, hypothesis testing, & confidence intervals). Prerequisites: Mathematics 211 and 213 each with a grade of C or better. 317/517

Mathematics    319

4 (crs.)

Infinite Processes for Teaching

An introduction to infinite processes; this course emphasizes modeling, problem solving, and communication. Topics include functions, continuity, limiting processes, rates of change, optimization, approximation of areas and volumes, sequences and series. (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 Abstract Algebra

This course offers an introduction to groups and rings, which are formed by associative operations on sets. A group has one operation, an identity, and inverses exist. Groups covered in this class include permutation, symmetric, alternating, and dihedral groups. Rings, which have addition and multiplication operations, arise naturally as generalized number systems. Rings covered in this class include matrices, integers modulo n, and polynomial rings. These algebraic systems have applications in art, biology, chemistry, combinatorics, computer science, geometry, linguistics, music, physics, and topology. 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 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 and 273 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 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 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 301 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 Teaching

An intuitive and investigative study of mathematical structure emphasizing modeling, problem solving, and communication. Topics include sets, operations, groups, and functions. Prerequisites: Mathematics 211 and 213 each with a grade of C or better. 413/613

Mathematics    415

4 (crs.)

Modern Geometry for Teaching

An intuitive and investigative study of geometry and axiomatics emphasizing modeling, problem solving, and communication. Topics are chosen from axiomatic systems, synthetic (constructive) geometry, transformational (motion) geometry (reflections, rotations, translations, and glide-reflections), analytic (coordinate) geometry, symmetry, fractal geometry, spatial visualization, topology and graph theory. Prerequisites: Mathematics 211 and 213 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    432

4 (crs.)

History and Philosophy of Mathematics and Math Education

Seminar emphasizing a study of research literature on the teaching and learning of mathematics, and on the history and philosophy of mathematics. Readings and discussions will focus on how has mathematics developed as a human discipline, the nature of mathematics and mathematical behavior, what we know about how people learn mathematics, and what all this means for the teaching of mathematics. Students will explore and discuss examples of ancient mathematics and classic proofs, compare and evaluate mathematics curricula, observe and analyze mathematics lessons, and will prepare and present a mathematics lesson. Prerequisites: Senior status with a major in Elementary Education and completion of 17 units (crs) toward a minor in Mathematics; or completion of 8 units (crs) in mathematics numbers 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 256. 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 non-routine 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 Math Teaching

Seminar emphasizing problem solving and mathematical modeling in Elem/Middle School, and Secondary programs. Survey and study of research literature on the teaching and learning of mathematics, and connections among the other courses in the mathematics minor and major programs. Experience with units from demonstration projects in school curriculum materials. Prerequisite: A major in elementary education and completion of 16 units (crs.) toward a minor in mathematics, or a major in mathematics and completion of 30 credits toward the major.

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).