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 departmentallymandated 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 singleradical 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 departmentallymandated 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 chisquare 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 quadraticinform, difference of squares, and sum and difference of cubes; quadratic and higherdegree 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, chisquare 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. Crosslisted with CSCI 231.




290 
Special Topics in Mathematics 
14 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; wellorderings, 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. Crosslisted 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 secondorder differential equations and applications; higher order linear differential equations; series solutions of secondorder 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, nonEuclidean, 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. Crosslisted 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, twodimensional 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. Crosslisted as CSCI 467.




490 
Special Topics in Mathematics 
13 cr 

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




495 
Senior Seminar 
12 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 
13 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 onesemester 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. Threehour lecture; onehour 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. Threehour lecture; onehour discussion; threehour 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. Threehour lecture; onehour discussion; threehour lab.




110 
Introduction to Astronomy 
3 cr 

Prereq: None. Freq: Fall, Spring.
Astronomy for nonscientists. Largely nonmathematical. Planets, stellar evolution, galactic systems, cosmology. Threehour 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. Crosslisted with ETHN 120. Threehour 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. Threehour lecture; onehour discussion; threehour 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. Threehour lecture; onehour discussion; threehour 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. Threehour 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 preengineering articulation agreement with UWMilwaukee.




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 preengineering articulation agreement with UWMilwaukee.




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, threephase circuits, and computeraided analysis. Required for the preengineering articulation agreement with UWMilwaukee (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 highlevel language, such as Python, with applications to science and engineering.




290 
Special Topics in Physics 
14 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, rigidbody dynamics, free and forced oscillations, normal coordinates, moving coordinate systems, generalized coordinates, Lagrangian and Hamiltonian formulations. Continuum mechanics. Fourhour 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. Fourhour 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. Threehour 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 opamps. Includes basic digital electronics. Sixhour 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, SturmLiouville 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. Fourhour 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 onedimensional 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. Fourhour lecture.




490 
Special Topics in Physics 
14 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 
13 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 physicsrelated 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 
12 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 
13 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.





