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Math and Physics

UW-PARKSIDE 2017-19 CATALOG

Molinaro 275 • 262-595-2316

College:
Natural and Health Sciences

Degree and Programs Offered:
Bachelor of Science

Majors - Mathematics, Physics

Minors - Mathematics, Physics

Professional Accreditations or Memberships:
American Mathematical Society

Student Organizations/Clubs:
Math Club; Pi Mu Epsilon (Wisconsin Gamma Chapter); Society of Physics Students

Career Possibilities for Mathematics Majors:
The future outlook for careers in mathematics remains promising, especially for those who combine their training with other specialties. A degree with a major in mathematics with supporting work in computer science, business or economics will increase employment opportunities.

Department Overview

The Mathematics and Physics Department offers a rigorous and well-balanced program of courses leading to a bachelor of science degree with majors in mathematics and physics. Mathematics is of central importance in the sciences. In fact, mathematics has been called the language of science. This applies not only to the physical and biological sciences but increasingly to the social, managerial and behavioral sciences as well. Much of mathematics has been developed to meet the needs of the areas of human knowledge that it serves. In addition to its service role in other areas, mathematics occupies a place of its own in our intellectual heritage. From ancient Greece to our own times, people have been drawn to the elegant structure.

The physics major is primarily intended for students who wish to pursue graduate work in physics or related areas, careers in higher education, or careers in technology-based industry.

The mathematics and physics faculty are active in research. Current areas of research interest include astrophysics, computational physics, condensed matter theory, many-body theory, mathematical physics, quantum field theory, and statistical mechanics. Students majoring in mathematics or physics have an excellent opportunity to get involved in ongoing research projects. In the recent past, students have appeared as co-authors on a number of scientific publications in research and teaching journals.

In addition to mathematics and physics majors, the department hosts an articulated pre-engineering/engineering program with the University of Wisconsin-Milwaukee.

Program Level Outcomes for Mathematics

  1. Formulate and prove mathematical results in the language of mathematics.
  2. Perform technical mathematical computations in mathematics and related fields.
  3. Translate ideas and meanings from the language of everyday life (English) into mathematical language (formulas and symbols).
  4. Communicate in the language of mathematics.
  5. Search for knowledge in independent and responsible ways.

Requirements for Admission to the Mathematics Major

To be eligible for entrance into the mathematics major students must have successfully  completed  MATH  221  and  222  with a grade of C or better in each, or at the discretion of the Department. Upon declaring a major in mathematics, students must consult with a mathematics adviser to set up a program of study.

Requirements for the Mathematics Major (41- 47 credits)

The major in mathematics includes options in pure and applied mathematics and teaching mathematics in middle childhood through early adolescence.  At least 15 credits of upper-level courses in the major must be completed at UW-Parkside. Students may satisfy a mathematics  major  by  completing the mathematics core and one of the following  options  or, upon consultation with a mathematics adviser, by developing programs to suit their special needs, subject to the written approval of the Mathematics Department. The following options are minimal, and students are encouraged to elect additional advanced mathematics courses.

  1. Core Courses Required (23 credits)
    These courses provide the background concepts and techniques required in upper-level mathematics offerings.

    MATH 221  Calculus and Analytic Geometry I 5 cr
    MATH 222 Calculus and Analytic Geometry II 5 cr
    MATH 223 Calculus and Analytic Geometry III 5 cr
    MATH 301 Linear Algebra 4 cr
    MATH 303 Set Theory, Logic and Proof  4 cr
  2. Choose One Option for Completion (20-24 credits)
    1. General Mathematics Option (20-24 credits)
      This sequence of courses leads to an undergraduate mathematics major covering the principal areas  of modern mathematics. It is recommended for students planning to study mathematics in graduate school. Students in this program are required to take all of the courses in the Mathematics Core in addition to  those listed below. Students are also encouraged to broaden their mathematics background by electing additional advanced courses.

      1. Required Math Courses (4 credits)
        Choose one course:  
        MATH 350 Advanced Calculus 4 cr
        MATH 451 Topology 4 cr
      2. 300-Level Math Elective 3 Courses (10-12 credits)
        MATH 310 Advanced Probability Theory and Statistics 4 cr
        MATH 317 Differential Equations and Their Applications 4 cr
        MATH 331 Logic and Combinatorics 3 cr
        MATH 361 Foundations of Geometry 3 cr
        MATH 367 Elementary Number Theory 4 cr
      3. 400-Level Math Elective (6-8 credits)
        Choose two 400-level courses
        (not MATH 495 or 499)
        6-8 cr
    2. Applied Mathematics Option (18 credits)
      This sequence of courses is intended for those students who are interested in mathematics and the application of mathematics. Students in this program are required to take all of the courses in the mathematics core together with those listed below. They are also encouraged to broaden their mathematics background by electing additional advanced courses.

      1. Required Math Courses (14 credits)
        MATH 310 Advanced Probability Theory and Statistics 4 cr
        MATH 317 Differential Equations and Their Applications 4 cr
        MATH 368 Mathematical Modeling 3 cr
             
        Choose one course:  
        MATH 401 Applied Mathematics 3 cr
        PHYS 401 Mathematical Methods of Physics 3 cr
      2. Math Elective Course (4 credits)
        Choose one course:  
        MATH 423 Complex Analysis 4 cr
        MATH 441 Abstract Algebra 4 cr

Teacher Education Licensure in Mathematics and Physics

Students interested in becoming teachers will need to complete an approved program pathway to a Wisconsin initial educator license. The approved pathway to this license is a structured collaboration between the mathematics and physics department and the Institute of Professional Educator Development (IPED).

The requirements for teacher licensure are specific and therefore students must meet with the IPED Adviser to coordinate the major and teacher education curriculum. It is very important to contact the IPED adviser at 262-595-2180 or Molinaro D111 as soon as possible. Students are required to seek advising each semester from both the IPED Adviser and the mathematics and physics department liaison to the teacher education program. Complete information about the Teacher Education Program can be found on the IPED website at: http://www.uwp.edu/learn/ departments/educatordevelopment/index.cfm

Mathematics with a Second Major

Students are encouraged to consider combining a major in mathematics with a major in a related area, such as computer science, behavioral science,  a  physical  science,  business or economics. This has the advantage of enhancing the understanding of two allied areas, as well as improving the prospects for employment after graduation.

Requirements for the Computer Science/ Mathematics Double Major (89-90 credits)

Students may satisfy graduation requirements for both computer science and mathematics by completing all required courses for computer science with 9 elective credits and PHYS 201, together with the following mathematics courses (which automatically satisfy the computer science breadth requirement):

Required Math Courses (30 credits)
MATH 222 Calculus and Analytic Geometry II 5 cr
MATH 223 Calculus and Analytic Geometry III 5 cr
MATH 301 Linear Algebra 4 cr
MATH 303 Set Theory, Logic and Proof 4 cr
MATH 317 Differential Equations and Their Applications 4 cr
     
MATH 350 Advanced Calculus 4 cr
OR    
MATH 367 Elementary Number Theory 4 cr
     
MATH 441 Abstract Algebra 4 cr

Students completing the computer science/mathematics double major are strongly encouraged to take CSCI 331 as one of their electives.

Requirements for the Mathematics Minor (25-27 credits)

To earn a mathematics minor students must complete a minimum of 25 credits in mathematics by completing the four required courses and at least two other upper level courses, one of which must be at the 400-level.

  1. Required Math Courses (19 credits)
    MATH 221 Calculus and Analytic Geometry I 5 cr
    MATH 222 Calculus and Analytic Geometry II 5 cr
    MATH 223 Calculus and Analytic Geometry III 5 cr
    MATH 301 Linear Algebra  4 cr
  2. Math 400-level Elective (3-4 credits)
    Choose one 400-level course (not MATH 495 or 499) 3-4 cr
  3. Math Additional Upper-level Elective (3-4 Credits)
    Choose one 300- or 400-level course
    (not MATH 495 or 499)
    3-4 cr

Requirements for the Elementary Mathematics Minor (31 credits)

To earn an elementary mathematics minor students must complete a minimum of 31 credits and have a declared elementary education or special education major.

  1. Required Math Courses (22-23 credits)
    MATH 221 Calculus and Analytic Geometry I 5 cr
    MATH 222 Calculus and Analytic Geometry II 5 cr
    MATH 223 Calculus and Analytic Geometry III 5 cr
         
    Choose one:    
    MATH 301 Linear Algebra 4 cr
    MATH 303 Set Theory, Logic and Proof 4 cr
         
    Choose one:    
    MATH 361  Foundations of Geometry 3 cr
    MATH 367 Elementary Number Theory

    4 cr

  2. Required Education Courses (9 credits)
    EDU 212  Mathematics for Elementary and Middle School Teachers 3 cr
    EDU 431 Teaching Developmental Math Concepts, K-2 3 cr
    EDU 442 Teaching Developmental Math Concepts, 3-8 3 cr

High School Preparation

Students entering a degree program at UW-Parkside should have taken at least three years of high school mathematics including ninth-grade algebra, 10th-grade geometry and 11th- grade advanced algebra and trigonometry. Students intending to take college-level mathematics courses are encouraged to strengthen their preparation by taking 12th-grade pre-calculus. MATH 10, MATH 11, MATH 15, MATH 16 and MATH 111 are not replacements for high school mathematics courses.

Computational Skills Requirement

Students satisfy this requirement with the completion of either MATH 102 or MATH 103 for 3 credits or MATH 111 for 4 credits (with a grade of C-minus or better).

Students are exempt from the requirement if their placement results (based on UW Mathematics Placement Test) are above MATH 102 or MATH 111. Students must complete computational skills within their first 60 academic credits.

Placement  Examination

Mathematics Placement is by UW Mathematics Placement Test scores. It is possible as well to take a placement test. This examination serves as a guide for placement in mathematics courses. Placement in mathematics courses is usually made at the following levels:

  1. MATH 10, MATH 15, MATH 102 , MATH 103 or MATH 111 – students with fewer than three years of high school math, or inadequate background, or who have been out of school for an extended period of time.
  2. MATH 112, MATH 113 or MATH 114 – students with three years of high school mathematics.
  3. MATH 221 – students with four years of high school mathematics.

Program Level Outcomes for Physics

  1. Student should be scientifically literate in the foundations of physics, both theoretical and practical.
  2. Students should be able to take data in a lab environment or computer simulation, analyze it, present it coherently in a written format and draw from the analysis a convincing conclusion based upon the principles of the scientific method.
  3. Students will master the tools of modern physics; mathematical, computational, and experimental.
  4. The student should be able to orally present in a professional, lucid manner, the results and analysis of an experiment or research and effectively answer questions on the topic of their work in a scientific seminar format
  5. The student is expected to have mastered the methods of modern scientific exploration at an appropriate level, and engage in a continual self-examination for any deficiencies, and take advantage of opportunities to rectify them. The goal is to be fully prepared for the Physics GRE exam.

Requirements for Admission to the Physics Major

To be eligible for entrance into the physics major students must have successfully completed MATH 221, 222 and PHYS 201, 202  with a grade of C or better in each, or at the discretion of the Department.

Requirements for the Physics Major (65 credits)

The physics major consists of at least 42 credits of core courses and a minimum of 23 credits of support courses, in addition to the general university requirements. At least 15 credits of upper level courses must be completed at UW-Parkside.

  1. Required Core Courses (42 credits)
    PHYS 201 General Physics I 5 cr
    PHYS 202 General Physics II 5 cr
    PHYS 205 Modern Physics 3 cr
    PHYS 241 Scientific Programming 3 cr
    PHYS 301 Classical Mechanics 4 cr
    PHYS 302 Electricity and Magnetism 4 cr
    PHYS 303 Computational Physics 3 cr
    PHYS 306 Advanced Experiments in Physics 3 cr
    PHYS 403 Thermodynamics and Statistical Physics 4 cr
    PHYS 441 Quantum Physics 4 cr
    PHYS 495 Senior Seminar 1 cr
         
    Choose one course:  
    PHYS 401 Mathematical Methods of Physics 3 cr
    MATH 401 Applied Mathematics 3 cr
  2. Required Support Courses (23 credits)
    MATH 221 Calculus and Analytic Geometry I 5 cr
    MATH 222 Calculus and Analytic Geometry II 5 cr
    MATH 223 Calculus and Analytic Geometry III 5 cr
    MATH 301 Linear Algebra 4 cr
    MATH 317 Differential Equations and Their Applications 4 cr
    Students planning graduate work in physics will generally take more than the minimum number of credit hours in physics and additional mathematics courses. Reading proficiency (equivalent to about two years of study at the college level) in one foreign language is also recommended for such students.

 

Requirements for the Physics Minor (32 credits)

  1. Required Physics Courses (16 credits)
    PHYS 201 General Physics I* 5 cr
    PHYS 202 General Physics II* 5 cr
    PHYS 205 Modern Physics 3 cr
    PHYS 306  Advanced Experiments in Physics 3 cr
  2. Physics Elective Courses (6 credits)
    Additional physics course at the 200-level or above 3 cr
    Additional physics course at the 300-level or above 3 cr
  3. Required Support Courses (10 credits)
    MATH 221  Calculus and Analytic Geometry I 5 cr
    MATH 222 Calculus and Analytic Geometry II 5 cr
    *Qualified students may substitute PHYS 105-106 for the PHYS 201-202 requirement at the discretion of the Physics Department. Students are advised to consult the department for further information.

Articulation Agreement

UW-MILWAUKEE ENGINEERING PROGRAM

The articulated pre-engineering/engineering agreement with University of Wisconsin-Milwaukee (UWM) creates a curriculum plan so the students at the University of Wisconsin-Parkside (UWP) may  complete   and   transfer  coursework  applicable to the first two years of the UWM electrical and mechanical engineering majors in the College of Engineering and Applied Science (CEAS), and provides guaranteed transfer to students who complete all of the articulated pre-engineering courses and the UWM admission requirements.

Admission Requirements and the Highlights of the Program

  • Students complete the first two years of course work (61-84 credits) at UW-Parkside, then continue at UWM for a degree in electrical engineering or mechanical engineering in the College of Engineering and Applied Science (CEAS) with junior standing.
  • The transfer with junior standing is guaranteed for students who complete all of the articulated pre-engineering courses with a cumulative GPA of 3.0 or above; and the UWM and CEAS admission requirements.
  • All UWP university admission requirements apply. Admission into the pre-engineering program requires placement into Math 221 or successful completion of the pre-requisites for Math 221.
  • During the first 61-84 c edits of study (the first two years), students will be primarily advised by UWP faculty but will also have a co-advisor from UWM to facilitate smooth transition to UWM CEAS.
  • Students will pay tuition and appropriate fees to the university at which they are enrolled.
  • Students admitted under this agreement will be guided by UWM and UWP catalog year of their admission to UWP.
  • Students who voluntarily withdraw or do not meet the requirement to continue in the program, may transfer any of their earned UWP/UWM credits into another degree program subject to the credit transfer equivalencies and requirements.

Mechanical Engineering 4-Year Plan

YEAR 1 AT UW-PARKSIDE (37-45 CREDITS)
Fall Semester (15 credits)
CHEM 101 General Chemistry I 4 cr
CHEM 103 General Chemistry Lab I  1 cr
MATH 221 Calculus and Analytic Geometry I 5 cr
PHYS 201 General Physics I 5 cr
Winterim Semester (3-7 credits)
Gen Ed Art or Hum or Soc 3 cr
  Foreign Lang*  4 cr

Spring Semester (16 credits)

MATH 222 Calculus and Analytic Geometry II 5 cr
PHYS 202 General Physics II 5 cr
PHYS 241 Scientific Programming 3 cr
PHYS 211 Statics 3 cr
Summer Semester (3-7 credits)
Gen Ed Art or Hum or Soc 3 cr
  Foreign Lang*  4 cr
YEAR 2 AT UW-PARKSIDE (30-36 CREDITS, 3 AT UWM)
Fall Semester (15 credits)
MATH 223 Calculus and Analytic Geometry III 5 cr
MATH 317 Differential Equations and Their Applications 4 cr
PHYS 212 Dynamics 3 cr
Gen Ed  Art or Hum or Soc 3 cr
Winterim Semester (3 credits)
ENGL  English Competency Requirement 3 cr
Spring Semester (15 credits)
CHEM 102 General Chemistry II 4 cr
CHEM 104 General Chemistry Lab II 1 cr
     
PHYS 303 Computational Physics 3 cr
OR    
MATH 368 Mathematical Modeling 3 cr
     
PHYS 403 Thermodynamics and Statistical Physics 4 cr
PHYS 214 Electrical Circuits I 3 cr
Summer Semester (6 credits)
Gen Ed Soc 3 cr
ENGL English Competency Requirement 3 cr
YEAR 3 AT UW-MILWAUKEE
Fall Semester (17 credits)
Civ Eng 303 Strength of Materials  (4 cr)
EAS 200 Professional Seminar (1 cr)
MechEng 110 Engineering Fundamentals I (4 cr)
MatlEng 201 Engineering Materials (4 cr)
MechEng 321 Basic Heat Transfer (4 cr)
Spring Semester (17 credits)
MechEng 111 Engineering Fundamentals II (4 cr)
MchEng 320 Intro to Fluid Mechanics (3 cr)
MatlEng 330 Materials and Processes in Manuf (3 cr)
Ind Eng 467 Intro Statistics/Phys Sci & Engr (3 cr)
MechEng 474 Intro to Control Systems (4 cr)
YEAR 4 AT UW-MILWAUKEE
Fall Semester (16 credits)
MechEng 323 Fluid Mechanics Laboratory (1 cr)
MechEng 360 Mechanical Design I (3 cr)
MechEng 366 Design of Machine Elements (4 cr)
MechEng 370 Comp Aided Engineer Lab (2 cr)
MechEng XXX Technical Elective (3 cr)
MechEng XXX Part B Oral & Written (3 cr)
Spring Semester (17 credits)
MechEng 438 Mech Eng Experimentation (3 cr)
MechEng 479 Mechatronics (3 cr)
MechEng 496 Senior Design (3 cr)
MechEng XXX Technical Electives (8 cr)

Electrical Engineering 4-Year Plan

YEAR 1 AT UW-PARKSIDE (37-45 CREDITS)
Fall Semester (15 credits)
CHEM 101  General Chemistry I 4 cr
CHEM 103 General Chemistry Lab I 1 cr
MATH 221 Calculus and Analytic Geometry I 5 cr
PHYS 201 General Physics I 5 cr
Winterim Semester (3-7 credits)
Gen Ed Art or Hum or Soc 3 cr
  Foreign Lang* 4 cr
Spring Semester (16 credits)
MATH 222 Calculus and Analytic Geometry II 5 cr
PHYS 202 General Physics II 5 cr
PHYS 211 Statics 3 cr
PHYS 241 Scientific Programming  3 cr
Summer Semester (3-7 credits)
Gen Ed Art or Hum or Soc 3 cr
  Foreign Lang* 4 cr
YEAR 2 AT UW-PARKSIDE (34-40 CREDITS, 3 AT UWM)
Fall Semester (16 credits)
MATH 223  Calculus and Analytic Geometry III 5 cr
MATH 317  Differential Equations and Their Applications 4 cr
PHYS 212 Dynamics 3 cr
PHYS 302 Electricity and Magnetism 4 cr
Winterim Semester (6 credits)
Gen Ed Art or Hum or Soc 3 cr
ENGL English Competency Requirement 3 cr
Spring Semester (15 credits)
CHEM 102  General Chemistry II 4 cr
CHEM 104 General Chemistry Lab II 1 cr
     
PHYS 303 Computational Physics 3 cr
OR    
MATH 368 Mathematical Modeling 3 cr
     
PHYS 403 Thermodynamics and Statistical Physics 4 cr
PHYS 214 Electrical Circuits I 3 cr
Summer Semester (6 credits)
Gen Ed Soc 3 cr
ENGL English Competency Requirement 3 cr
YEAR 3 AT UW-MILWAUKEE
Fall Semester (15 credits)
Commun XXX Part B Oral & Written (3 cr)
EAS 200 Professional Seminar (1 cr)
ElecEng 305 Electrical Circuits II (4 cr)
ElecEng 354 Digital Logic (3 cr)
MatlEng 201 Engineering Materials (4 cr)
Spring Semester (15 credits)
ElecEng 310  Signals and Systems  (3 cr)
ElecEng 330 Electronics I   (4 cr)
ElecEng 362 Electromechanical Energy Conv (4 cr)
ElecEng 367 Intro to Microprocessors (4 cr)
YEAR 4 AT UW-MILWAUKEE
Fall Semester (16 credits)
ElecEng 335 Electronics II (4 cr)
ElecEng 420 Random Signals and Systems (3 cr)
ElecEng XXX Technical Electives (9 cr)
Spring Semester (13 credits)
ElecEng 595  Senior Design (4 cr)
ElecEng XXX Technical Electives (9 cr)

*If required, refer to UWM foreign language requirement

Note: Students should work with their advisers and utilize TIS to determine general education courses that transfer to UWM and meet UWM general education requirements.

Courses in Mathematics (MATH)

10 Essential Math Skills 3 cr
 

Prereq:  None. Freq: Fall, Spring.
Reviews basic arithmetic and order of operations with integers, fractions and decimals. Includes applied proportions and percents; evaluation and simplification of algebraic expressions and geometric formulas; linear equations involving integers, fractions and decimals; positive exponents; greatest common factor; basic graphs and inequalities.Course graded on credit/no credit basis. A grade of CR is required to advance to the next level (MATH 15). Four hour lecture; supplemental discussion as warranted by individual student course performance.

     
11  Essential Math Skills Lab 2 cr
 

Prereq:  Completion of departmentally-mandated minimal number of MATH 10 proficiencies.  Consent of instructor required. Freq:  Winterim, Summer.
Designed as a Winterim/Summer opportunity for students to satisfy a limited number of incomplete proficiencies from an immediately prior Fall/Spring MATH 10 without having to retake MATH 10 in its entirety. Course graded on credit/no credit basis.

     
15 Intermediate Algebra 4 cr
 

Prereq: MATH 10 with a grade of C or better or a grade of CR; or MATH 11 with a grade of CR; or appropriate placement score. Freq: Fall, Spring.
Covers linear equations and inequalities with applications; equations of lines and linear systems with applications; exponential and polynomial operations with introduction to functions; polynomial factoring by combinations of GCF, grouping, trinomial, and difference of squares; quadratic equations by factoring with applications; rational operations and equations with applications; radical operations and single-radical equations; square root property and quadratic formula for quadratic equations.  Course graded on credit/no credit basis. A grade of CR is required to proceed to the next level (MATH 102 or 111). Five hour lecture; supplemental discussion as warranted by individual student course performance.

     
16 Intermediate Algebra Lab 2 cr
 

Prereq:  Completion of departmentally-mandated minimal number of MATH 15 proficiencies.  Consent of instructor required. Freq:  Winterim, Summer.
Designed as a Winterim/Summer opportunity for students to satisfy a limited number of incomplete proficiencies from an immediately prior Fall/Spring MATH 15 without having to retake MATH 15 in its entirety. Course graded on credit/no credit basis.

     
102 Survey of Mathematics 3 cr
 

Prereq:  MATH 15 or 16 with a minimum grade of C/CR; or appropriate placement. Freq: Fall.
Covers topics selected from sets, logic, number theory, geometry, consumer math, linear and exponential modeling, math and the arts, voting methods, probability, and statistics. Intended for student who need no further mathematics courses beyond competency.

     
103 Elementary Statistics 3 cr
 

Prereq: MATH 15 or 16 with a minimum grade of C/CR; or appropriate placement. Freq: Fall, Spring.
Introduces modern statistics including descriptive statistic; binomial and normal distributions, estimation, hypothesis testing; and an introduction to the z, t, F and chi-square test statistics. Includes computerized data analysis. Three hours lecture.

     
111 College Algebra I 4 cr
 

Prereq: MATH 15 or 16 with a minimum grade of C/CR; or appropriate placement. Freq: Fall, Spring.
Studies linear equations, single and compound inequalities, and absolute value equations and inequalities; exponential and polynomial operations with function evaluation; polynomial factoring by combinations of GCF, grouping, trinomial including quadratic-in-form, difference of squares, and sum and difference of cubes; quadratic and higher-degree equations by factoring with applications; rational operations and equations with applications; variation; radical operations and equations with up to two radical terms; complex numbers; completing the square and quadratic formula for quadratic equations; general polynomial equations; quadratic functions with graphing and applications; introduction to exponential and logarithmic functions and equations.

     
112 College Algebra II 4 cr
 

Prereq: MATH 111 with a grade of C or better; or equivalent; or appropriate placement score. Freq: Fall, Spring.
Explores functions and graphs, polynomial functions, exponential and logarithmic functions, sequences, series, induction and combinatorics. Four hours lecture.

     
113 Trigonometry 2 cr
 

Prereq: MATH 112 or equivalent or concurrent registration. Freq: Fall, Spring.
An introduction to trigonometry with applications. Angular and circular definitions of trigonometric functions, graphing, use of fundamental identities.

     
114 College Algebra II with Trigonometry 5 cr
 

Prereq: MATH 111 with a grade of C or better; or equivalent; or appropriate placement  score.  Freq:  Fall, Spring.
Functions and graphs, polynomials and rational functions, exponential and logarithmic functions, trigonometric functions, trigonometric identities and equations, applications, sequences, series. Not open to those with credit in MATH 112 or 113.

     
203 Intermediate Statistics 3 cr
 

Prereq: Successfully complete the computational skills requirement. Freq: Spring.
Introduces inferential statistics including elementary combinatorics and probability, binomial and normal distributions, Central Limit Theorem, estimation, confidence internals, hypothesis testing, correlation, regression, chi-square distribution, and analysis of variance.

     
214 Mathematics for Middle Childhood Through Early Adolescence Teachers I  5 cr
 

Prereq: MATH 111 with a grade of C or better; or consent of instructor. Freq: Occasionally.
Topics include the development of the algorithms of arithmetic, numeration systems, problem solving, number theory and set theory.

     
215 Mathematics for Middle Childhood Through Early Adolescence Teachers II 5 cr
 

Prereq: MATH 215. Freq: Occasionally.
Topics include introductory geometry, constructions, congruence, similarity, motion geometry, concepts of -measurements, probability and statistics.

     
221 Calculus and Analytic Geometry I 5 cr
 

Prereq: MATH 112 and 113 or equivalent or appropriate placement score. Freq: Fall, Spring.
Explains rate of change and limits, differentiation, applications of the derivative, integration, applications of the integral and transcendental functions.

     
222 Calculus and Analytic Geometry II 5 cr
 

Prereq: MATH 221. Freq: Fall, Spring.
Explains methods of integration, analytic geometry, polar coordinates, hyperbolic functions, infinite series, power series, and introduction to ordinary differential equations.

     
223 Calculus and Analytic Geometry III 5 cr
 

Prereq: MATH 222. Freq: Fall.
Explains vectors and parametric equations, vector functions and their derivatives, partial and directional derivatives, multiple integrals, vector analysis, Green’s Theorem and Stokes’ Theorem.

     
231 Discrete Mathematics  3 cr
 

Prereq: MATH 112 with a C or better.  Freq: Fall, Spring.
Sets; the number system; Boolean algebra; formal logic and proofs; relations and functions; combinatorics and recurrence relations; graphs and trees.  Cross-listed with CSCI 231.

     
290 Special Topics in Mathematics 1-4 cr
 

Prereq: None. Freq: Occasionally.
Selected topics in mathematics will be examined.

     
301 Linear Algebra 4 cr
 

Prereq: MATH 223 or MATH 222 and consent of instructor. Freq: Fall.
Introduction  to linear algebra including  systems of -equations, matrices, determinants, vector spaces and linear transformations, and diagonalization.

 
     
303  Set Theory, Logic and Proof 4 cr
 

Prereq: MATH 222; or PHIL 201 and consent of instructor. Freq: Fall, Spring.
Examines the elementary propositional and predicate logic; language and axioms of set theory; operations on sets; well-orderings, ordinals, transfinite induction and recursion; cardinals; the axiom of choice; combinatorics; reading and writing of proofs in mathematics. Cross- listed with PHIL 303.

     
309 Probability and Statistics 3 cr
 

Prereq: MATH 221 with a grade of C or better; or consent of instructor. Freq: Spring.
Covers elementary probability; random variables, properties of distributions, sampling, queuing theory, central limit theorem and law of large numbers. Cross-listed with CSCI 309.

     
310 Advanced Probability Theory and Statistics 4 cr
 

Prereq: MATH  223. Freq: Fall.
The main mathematical methods and techniques of probability theory; random variables, expected values, variance, central limit theorem, parameter estimation, and hypothesis testing.

 
     
317 Differential Equations and Their Applications 4 cr
 

Prereq: MATH 222. Freq: Fall.
First- and second-order differential equations and applications; higher- order linear differential equations; series solutions of second-order differential equations; Laplace transforms; matrix algebra, systems of equations, eigen values and eigenvectors; systems of differential equations; and partial differential equations. Not open to those with credit in MATH 321.

     
331 Logic and Combinatorics 3 cr
 

Prereq:  MATH 222. Freq: Yearly.
Permutations and combinations, graphs, trees, mathematical induction, propositional calculus, Mathematica and its applications in combinatorics, number theory and linear programming. Intended for students working for teaching certification in mathematics.

     
350 Advanced Calculus 4 cr
 

Prereq: MATH 223, 303. Freq: Spring.
Covers the fundamental notions of limits, continuity, uniform continuity, derivative, and integral. Examines infinite series with a study of convergence and uniform convergence.

     
361 Foundations of Geometry 3 cr
 

Prereq: MATH 222. Freq: Yearly.
Introduction to axiomatic geometry including Euclidean, non-Euclidean, and projective geometries.

     
367 Elementary Number Theory 4 cr
 

Prereq: MATH 222. Freq: Spring.
Prime numbers, fundamental theorem of arithmetic, congruence, quadratic residues and quadratic reciprocity, partitions, number theoretic functions and diophantine equations.

     
368 Mathematical Modeling 3 cr
 

Prereq: MATH 222; PHYS 241 or CSCI 130 or consent of instructor. Freq: Yearly.
Survey of mathematical models, models involving -differential equations, probabilistic models, Markovian -models, simulation, and Monte Carlo methods. Cross-listed with CSCI 368.

     
373 History of Mathematics 3 cr
 

Prereq: MATH 221 or consent of instructor. Freq: Occasionally.
Main lines of mathematical development from the Babylonians, Egyptians and Greeks  to  the  present  day; the  lives  of  great  mathematicians: Euclid, Archimedes, Descartes, Newton, Gauss, Cantor.

     
401 Applied Mathematics 3 cr
 

Prereq: MATH 222, 301. Freq: Fall (odd years).    
Explores traditional analytical and numerical methods enriched by modern mathematical developments and applications to various fields such as ocean and atmospheric sciences. Combines approximate forms of the basic mathematical equations of motion with analysis.

     
421 Real Analysis 4 cr
 

Prereq: MATH 350. Freq: Occasionally.
Construction of the real number system; basic theory of metric spaces; fundamental notions of limit, continuity, uniform continuity and basic theorems concerning these; convergence and uniform convergence; differentiation and the Riemann integral.

     
422 Topics in Real Analysis 4 cr
 

Prereq: MATH 421. Freq: Occasionally.
Differentials and Jacobians; implicit and inverse function theorems; introduction to the Lebesque integral; additional topics chosen in accordance with the interests and needs of the participants.

     
423 Complex Analysis 4 cr
 

Prereq: MATH 223, 303. Freq: Spring.
Examines elementary functions of a complex variable; analytic -functions; complex integrals and residue theory; conformal mapping; applications to electrostatics and hydrodynamics.

     
441 Abstract Algebra 4 cr
 

Prereq: MATH 301, MATH 303; or consent of instructor. Freq: Fall.
A study of group theory which includes subgroups, normal subgroups, isomorphisms, quotient groups, Cayley’s Theorem, and Lagrange’s Theorem. Provides an introduction to ring theory which includes subrings, ideals and factor rings, and polynomial rings.

     
442 Topics in Abstract Algebra 4 cr
 

Prereq: MATH 441. Freq: Occasionally.
Rings and ideals; fundamental theorems of Abelian groups; Sylow theorems; solvable groups; elements of Galois theory; solvability by radicals; characteristic roots, matrices and canonical forms. Additional topics chosen in accordance with the needs and interests of the participants, e.g. applications of group theory.

     
451 Topology 4 cr
 

Prereq: MATH 301, MATH 303; or consent of instructor. Freq: Spring.
Introduction to the theory of topological spaces, metric spaces, continuous functions, two-dimensional manifolds, and the concept of the fundamental group.

     
461 Differential Geometry 3 cr
 

Prereq: MATH 301, 350. Freq: Occasionally.
Local theory of curves and surfaces, curvature tensors, and global theory of surfaces.

     
467 Computability and Automata 3 cr
 

Prereq: MATH/CSCI 331 with a grade of C or better. Freq: Occasionally.
Turing machines, recursive functions, Kleene’s T Predicate, Ackermann’s functions, finite automata, grammars and languages. Cross-listed as CSCI 467.

     
490 Special Topics in Mathematics 1-3 cr
 

Prereq: Consent of instructor. Freq: Occasionally.
Intensive treatment of various specialized areas of mathematics.

     
495 Senior Seminar 1-2 cr
 

Prereq: Senior standing and consent of instructor. Freq: Occasionally.
Research and presentation of selected topics from the mathematical literature. One hour discussion.

     
499 Independent Study 1-3 cr
 

Prereq: Consent of instructor and department chair. Freq: Occasionally.

 
     

Courses in Physics (PHYS)

101  Principles of Physics 4 cr
 

Prereq: Computational Skills required or equivalent. Freq: Fall, Spring.
A  one-semester  introduction  to  fundamental  principles  of  physics, their  experimental  basis,  and  applications.  For students who need an introductory course in physics. Not open to students with credit in PHYS 105 or 201. Three-hour lecture; one-hour discussion.

     
105 College Physics I 5 cr
 

Prereq: MATH 113, 114 or equivalent. Freq: Fall.
Mechanics, heat, and sound. Not recommended for students majoring in physical science or engineering. Not open to students with credit in PHYS 201. Three-hour lecture; one-hour discussion; three-hour lab.

     
106  College Physics II 5 cr
 

Prereq: PHYS 105. Freq: Spring.
Electricity and magnetism, light and modern physics. Not open to students with credit in PHYS 202. Three-hour lecture; one-hour discussion; three-hour lab.

     
110 Introduction to Astronomy 3 cr
 

Prereq: None. Freq: Fall, Spring.
Astronomy for non-scientists.  Largely non-mathematical. Planets, stellar evolution, galactic systems, cosmology. Three-hour lecture.

     
120 Astronomy of Native America 3 cr
 

Prereq: None. Freq: Fall, Spring.
Examines the astronomical views of Native Americans from a cultural perspective and looks at how worldview, science and discrimination intersect. Current cultural conflicts between Western astronomers and Native groups and the growth of modern astronomy from the astronomies of indigenous cultures will be examined. Cross-listed with ETHN 120. Three-hour lecture.

     
150 Physics of Music 3 cr
 

Prereq: None. Freq: Occasionally.
An introduction to the basic physical principles underlying music and musical instruments. Not for credit towards the physics major.

     
201 General Physics I 5 cr
 

Prereq: MATH 221 with a grade of C or better; or concurrent registration. Freq: Fall.
Mechanics, heat, and sound. For physical science and engineering majors. Three-hour lecture; one-hour discussion; three-hour lab.

     
202 General Physics II 5 cr
 

Prereq: PHYS 201; MATH 222 or concurrent registration. Freq: Spring.
Electricity and magnetism, geometrical optics, and physical optics. For physical science and engineering majors. Three-hour lecture; one-hour discussion; three-hour lab.

     
205 Modern Physics 3 cr
 

Prereq: PHYS 202. Freq: Fall.
Special relativity. Elements of quantum mechanics. Introduction to atomic, molecular, solid state, nuclear, and particle physics. Three-hour lecture.

     
211 Statics 3 cr
 

Prereq: MATH 221 with grade of C or better, concurrent registration in MATH 222. Freq: Spring.
Discusses vectors, equilibrium of a particle, resultants of force systems, equilibrium of rigid bodies in two and three dimensions, structural analysis, friction, centroids, and moments in inertia. Required for the pre-engineering articulation agreement with UW-Milwaukee.

     
212 Dynamics 3 cr
 

Prereq: MATH 222 with a grade of C or better, concurrent registration in MATH 223, PHYS 211. Freq: Fall.
Covers motion and the laws of motion in different dimensions of space using various orthogonal curvilinear coordinates; relative motion; work and energy; conservative forces and potential energy; conservation of linear and angular momentum; and rigid body motion. Required for the pre-engineering articulation agreement with UW-Milwaukee.

     
214 Electrical Circuits I 3 cr
 

Prereq: PHYS 202 with a grade of C or better. Freq: Spring.
Covers circuit laws and analysis, restrictive circuits, energy storage, AC circuits and power, three-phase circuits, and computer-aided analysis. Required for the pre-engineering articulation agreement with UW-Milwaukee (equivalent to UWM ElecEng 301).

     
241 Scientific Programming 3 cr
 

Prereq: PHYS 201; MATH 221 or consent of instructor. Freq: Spring.
Studies programming in MATLAB and another high-level language, such as Python, with applications to science and engineering.

     
290 Special Topics in Physics 1-4 cr
 

Prereq: Consent of instructor. Freq: Occasionally.
Special topics in physics will be examined.

     
301 Classical Mechanics 4 cr
 

Prereq: PHYS 201 and 202 with grades of C or better; MATH 317, or concurrent registration; or consent of instructor. Freq: Fall (even years).
Vector analysis, conservation laws, planetary motion, rigid-body dynamics, free and forced oscillations, normal coordinates, moving coordinate systems, generalized coordinates, Lagrangian and Hamiltonian formulations. Continuum mechanics. Four-hour lecture.

     
302 Electricity and Magnetism 4 cr
 

Prereq: PHYS 201 and 202 with grades of C or better; MATH 317, or concurrent registration; or consent of instructor. Freq: Fall.
Electrostatics, magnetostatics, electromagnetic fields through Maxwell’s equations with basic applications. Radiation, Lienard- Wiechert potentials, sources of radiation, antenna theory. Scalar diffraction theory. Wave optics for transparent or conductive media. Four-hour lecture.

     
303 Computational Physics 3 cr
 

Prereq: PHYS 201 and 202 with grades of C or better; PHYS 205, 241; MATH 223; or consent of instructor. Freq: Spring.
Introduces computational physics with applications to classical mechanics, electromagnetism, and quantum mechanics. Monte Carlo methods. Introduces molecular dynamics. Three-hour lecture.

     
306 Advanced Experiments in Physics 3 cr
 

Prereq: PHYS 201 and 202 with grades of C or better; PHYS 205. Freq: Spring (odd years).
Covers advanced experiments in optics, atomic, molecular, solid state, and nuclear physics. Examines analog electronics through transistors and op-amps. Includes basic digital electronics. Six-hour lab.

     
401 Mathematical Methods of Physics 3 cr
 

Prereq: MATH 222, 301. Freq: Fall (even years).
Applies mathematical methods to various areas of the physical sciences with emphasis on physics. Covers a wide range of mathematical methods, including vector and tensor analysis and coordinate transformations, complex variables, Fourier series and integral transforms, Sturm-Liouville systems and orthogonal functions, partial differential equations, calculus of variations, and probability and statistics.

     
403 Thermodynamics and Statistical Physics 4 cr
 

Prereq: PHYS 201 and 202 with grades of C or better; PHYS 205; MATH 301 and 317 or PHYS 401 or consent of instructor. Freq: Spring.
Introduces equilibrium statistical mechanics and its applications. Emphasizes thermodynamics and classical statistical mechanics, microcanonical, canonical, and grand canonical ensembles, partition functions, the Ising model, quantum statistical mechanics, Fermi and Bose gases, and critical phenomena. Four-hour lecture.

     
441 Quantum Physics 4 cr
 

Prereq: PHYS 201 and 202 with grades of C or better; PHYS 205; MATH 301 and 317 or PHYS 401; or consent of instructor. Freq: Spring (odd years).
Explores quantum mechanics, free particle in wave mechanics, particles in one-dimensional potentials, axiomatic foundations of quantum mechanics, the evolution of states in time, particles in three dimensions, angular momentum, and central potentials. Introduces the concept of spin and the exclusion principle, and the Dirac equation with its associated phenomenology. Four-hour lecture.

     
490  Special Topics in Physics 1-4 cr
 

Prereq: PHYS 201 and 202 with grades of C or better and consent of instructor. Freq: Occasionally.
Examines special topics in physics.

     
494 Internship in Physics 1-3 cr
 

Prereq: PHYS 201 and 202 with grades of C or better; GPA of 2.5 or higher; and consent of instructor. Freq: Fall, Spring, Summer.
Work in a physics-related position under joint supervision of a physics faculty and a member of the sponsoring public or private organization.

     
495  Senior Seminar 1 cr
 

Prereq: PHYS 201 and 202 with grades of C or better; junior or senior standing. Freq: Fall, Spring.
A directed study of one of the current topics in physics. Students are recommended to take two consecutive semesters of 495.

     
497 Senior Thesis 1-2 cr
 

Prereq: PHYS 201 and 202 with grades of C or better; and consent of instructor. Freq: Occasionally.
Investigates advanced topics in physics.

     
499 Independent Study 1-3 cr
 

Prereq: PHYS 201 and 202 with grades of C or better; consent of instructor and department chair. Freq: Occasionally.
Investigates advanced topics in physics.

 
     

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