Wisconsin's Public Liberal Arts College

Mathematics


2012-2014 Catalog

Mathematics

Faculty and Academic Staff

Sergei Bezroukov, Professor
Uwe Leck, Associate Professor
Shaun M. Lynch, Professor
Steven J. Rosenberg, Associate Professor
Chad H. Scott, Professor
Shin-Ping Tucker, Associate Professor

Academic Staff
Marilyn Toscano, Senior Lecturer

Mathematics Program

Courses are offered in Computer Science, Mathematics, and Mathematics Education. The curriculum provides fundamental courses as well as a variety of electives for those with special interests. Students may choose a major that prepares them for a career and/or graduate study in Computer Science, Mathematics or Mathematics Education. Students also can pursue a career in Actuarial Science or Computer Security with appropriate choices of elective courses. More details on programs offered by the Department of Mathematics and Computer Science are presented below and at http://www.uwsuper.edu/acaddept/mathcsci.

Mathematics major programs include Liberal Arts, Discrete Applied Mathematics (comprehensive, no minor required), and Secondary Education. Mathematics minor programs include Liberal Arts, Secondary Education and Elementary Education. All major programs permit choices of courses appropriate to individual interests, which should be made in consultation with a Mathematics and Computer Science faculty advisor.

Preparation for Graduate Study

Students who intend to do graduate work in mathematics should include both MATH 440 and 455 in their course selections when completing one of the major programs above. Many graduate schools require the Graduate Record Examination (GRE) Advanced Mathematics Test.

Actuarial Science

Students of Mathematics can find a rewarding career as an actuary in finance, insurance or any of a wide variety of industries requiring risk analysis and assessment. These courses are recommended: MATH 240, 241, 242, 310, 370, 371; ECON 250, 251; FIN 320, 420, 426; ACCT 200. In general, students should take a broad spectrum of courses in Accounting, Economics, Political Science, Finance and Business Administration as well as Mathematics and Computer Science. Interested students should contact Dr. Steven Rosenberg in the Department of Mathematics and Computer Science.

Internship and Professional Practice

Students who major in programs offered by the Department of Mathematics and Computer Science have opportunities for paid work related to their field of study. Prerequisite: Junior standing and approval by the Mathematics and Computer Science faculty.

Student Learning Outcomes

Mathematics Major

  • Applies an appropriate formal process (or formal language) to write a solution to a given problem and to evaluate the validity and effectiveness of a given written solution.
  • Solves multi-part problems by performing appropriate analysis and complex calculations.
  • Demonstrates fluency in the definitions, results, analysis, and reasoning of a given axiomatically defined system.
  • Produces a well-written article synthesizing existing results or providing original results spanning multiple areas of mathematics

Discrete Applied Mathematics Major

  • Applies an appropriate formal process (or formal language) to write a solution to a given problem and to evaluate the validity and effectiveness of a given written solution.
  • Solves multi-part problems by performing appropriate analysis and complex calculations.
  • Understands and effectively utilizes both high and low-level programming concepts and languages.
  • Demonstrates fluency in the definitions, results, analysis, and reasoning of a given axiomatically defined system.
  • Produces a well-written article synthesizing existing results or providing original results spanning multiples areas of mathematics.

Mathematics Majors

Mathematics Major Requirements

Mathematics Major (Liberal Arts) prepares students for careers in mathematics, science and research, or for graduate study.

36 total credits

Core required courses (22 credits required):

CSCI 201 Introduction to Programming -- 3 credits
MATH 240 Calculus and Analytic Geometry I -- 4 credits
MATH 241 Calculus and Analytic Geometry II -- 4 credits
MATH 242 Calculus and Analytic Geometry III -- 4 credits
MATH 310 Introduction to Abstract Mathematics -- 3 credits
MATH 315 Linear Algebra -- 3 credits
MATH 498 Mathematics Capstone -- 1 credit

Probability, Statistics or Modeling required course (3 credits required):

MATH 370 Probability -- 3 credits
MATH 371 Statistics -- 4 credits
MATH 380 Introduction to Mathematical Modeling -- 4 credits

Advanced Topics required courses (8 credits required):

MATH 421 Theory of Computation -- 4 credits
MATH 437 Cryptography -- 4 credits
MATH 440 Real Analysis -- 4 credits
MATH 450 Topology -- 4 credits
MATH 455 Abstract Algebra -- 4 credits
MATH 471 Introduction to Complex Variables -- 4 credits

Math Upper-Division required course (3 credits required): At least one additional MATH course numbered 300 or above.

Discrete Applied Mathematics Concentration (comprehensive) Requirements

The Discrete Applied Mathematics concentration provides the tools used in many everyday activities in science and industry. Many objects and notions in the modern world are discrete in their nature and require special methods for their study. Research directions that are based mostly on the discrete approach include: coding theory and cryptography, data protection and compression, network analysis, parallel computing, logic, theory of computation, discrete and combinatorial optimization, scheduling theory, programming language design, and many others. Continuous methods of classical mathematics are, as a rule, largely inapplicable to these areas. Many of these fields are actually at the border between mathematics and theoretical computer science. This concentration offers a number of exciting courses that are intended for those who are interested in computers and mathematics. Computer science is not limited to programming. It uses discrete mathematics methods extensively to find more efficient solutions. Discrete mathematics has grown from everyday practical problems, and knowing efficient approaches to solving them has been found to be very beneficial.

54 total credits

Math Core required courses (48 credits required):

MATH 240 Calculus and Analytic Geometry I -- 4 credits
MATH 241 Calculus and Analytic Geometry II -- 4 credits
MATH 242 Calculus and Analytic Geometry III -- 4 credits
MATH 310 Introduction to Abstract Mathematics -- 3 credits
MATH 315 Linear Algebra -- 3 credits
MATH 320 Discrete Structures -- 4 credits
MATH 370 Probability -- 3 credits
MATH 498 Mathematics Capstone -- 1 credit
MATH 455 Abstract Algebra -- 4 credits
MATH 425
Algorithm Design & Analysis -- 4 credits
CSCI 201
Introduction to Programming -- 3 credits
CSCI 202 Object-Oriented Programming -- 3 credits
CSCI 303 Algorithms and Data Structures -- 4 credits
 CSCI 421 Theory of Computation -- 4 credits

Math and Computer Science Elective courses (6 credits required): at least two additional courses in MATH or CSCI numbered 300 or above.

Mathematics Teaching Major - Early Adolescence-Adolescence Level (EA-A) Requirements

35 total credits

Math required courses (21 credits required):

MTHEd 170 Programming and Technology for the Teaching of Mathematics -- 3 credits
MATH 240 Calculus and Analytic Geometry I -- 4 credits
MATH 241 Calculus and Analytic Geometry II -- 4 credits
MATH 242 Calculus and Analytic Geometry III -- 4 credits
MATH 310 Introduction to Abstract Mathematics -- 3 credits
MATH 315 Linear Algebra -- 3 credits
MATH 362 Topics in Geometry -- 3 credits

Special Topic required course (4 credits required):

MATH 320 Discrete Structures -- 4 credits
MATH 344 Differential Equations -- 4 credits

Statistics/Probability required course (3 credits required):

MATH 370 Probability -- 3 credits
MATH 371 Statistics -- 4 credits

Advanced Level Mathematics required course (4 credits required):

MATH 421 Theory of Computation -- 4 credits
MATH 437 Cryptography -- 4 credits
MATH 440 Real Analysis -- 4 credits
MATH 455 Abstract Algebra -- 4 credits
MATH 471 Introduction to Complex Variables -- 4 credits

Math Education required course (3 credits required):

MTHEd 339 Teaching Mathematics/Computer Science in the Secondary School -- 3 credits
MTHEd 305 Tutor Practicum -- 1-3 credits

All EA-A licensure students must also meet the Professional Education Requirements as outlined in the Teacher Education Certification section of this catalog. Students are also required to pass a subject specific Praxis II exam designated by the Wisconsin Department of Public Instruction before being placed for student teaching.

Mathematics Minor Requirements

21 total credits

Math required courses (11 credits required):

MATH 240 Calculus and Analytic Geometry I -- 4 credits
MATH 241 Calculus and Analytic Geometry II -- 4 credits
MATH 310 Introduction to Abstract Mathematics -- 3 credits

Computer Science/Math Education required course (3 credits required):

MTHEd 170 Programming and Technology for the Teaching of Mathematics -- 3 credits
CSCI 201 Introduction to Programming -- 3 credits

Math Elective courses (7 credits required):

MATH 242 Calculus and Analytic Geometry II
OR
Mathematics courses numbered 300 or above.

Mathematics Teaching Minor -- Early Adolescence-Adolescence Level (EA-A) Requirements

24 credits total credits

Math required courses (18 credits required):

MTHEd 170 Programming and Technology for the Teaching of Mathematics -- 3 credits
MATH 240 Calculus and Analytic Geometry I -- 4 credits
MATH 241 Calculus and Analytic Geometry II -- 4 credits
MATH 242 Calculus and Analytic Geometry III -- 4 credits
MATH 310 Introduction to Abstract Mathematics -- 3 credits
MATH 362 Topics in Geometry -- 3 credits

Math Elective courses (3 credits required):

MATH 315 Linear Algebra -- 3 credits
MATH 370 Probability -- 3 credits
MATH 371 Statistics -- 4 credits

Math Education required course (3 credits required):

MTHEd 339 Teaching Mathematics/Computer Sciencein the Secondary School -- 3 credits
MTHEd 305 Tutor Practicum -- 1-3 credits

All EA-A licensure students must also meet the Professional Education Requirements as outlined in the Teacher Education Certification section of this catalog. Students are also required to pass a subject specific Praxis II exam designated by the Wisconsin Department of Public Instruction before being placed for student teaching.

Mathematics Teaching Minor - Middle Childhood-Early Adolescence (MC-EA) Requirements

23 total credits

Required courses (23 credits required):

MTHEd 170 Programming and Technology for theTeaching of Mathematics -- 3 credits
MATH 130 Elementary Statistics -- 4 credits
MTHEd 230 Foundations of Mathematics for Elementary Education I -- 3 credits
MATH 240 Calculus and Analytic Geometry I -- 4 credits
MATH 310 Introduction to Abstract Mathematics -- 3 credits
MTHEd 322 Using Mathematical Learning Processes in the Elementary/Middle School Content Areas -- 3 credits
MATH 362 Topics in Geometry -- 3 credits

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