Math and Physics

Essential Math Skills
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.

Essential Math Skills Lab
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.

Intermediate Algebra
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.

Intermediate Algebra Lab
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.

Survey of Mathematics
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 students who need no further mathematics courses beyond competency.

Elementary Statistics
Prereq: MATH 15 or 16 with a minimum grade of C/CR; or appropriate placement. Freq: Fall, Spring.
Introduces modern statistics including descriptive statistics; 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-hour lecture. Not open to students with credits in any of these courses: BIOS 210, CRMJ 200, GEOG 300, GEOS 295, MATH 203, POLS 200, PSYC 250, QM 210, 310, SOCA 250, 295, 300.

Quantitative Reasoning
Prereq: MATH 15 or 16 with a minimum grade of C/CR; or appropriate placement. Freq: Fall.
Covers quantitative reasoning including topics from college algebra (such as functions, linear, exponential and logarithmic models), statistics, and probability. Emphasizes proportional reasoning, modeling, problem-solving and applications. Designed for students in programs that do not require further coursework in pre-calculus or calculus. Three-hour lecture; one-hour discussion required for some students based on placement.

College Algebra I
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.

College Algebra II
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-hour lecture.

Trigonometry
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.

College Algebra II with Trigonometry
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.

Intermediate Statistics
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.

Mathematics for Middle Childhood Through Early Adolescence Teachers I
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.

Mathematics for Middle Childhood Through Early Adolescence Teachers II
Prereq: MATH 215. Freq: Occasionally.
Topics include introductory geometry, constructions, congruence, similarity, motion geometry, concepts of measurements, probability and statistics.

Calculus and Analytic Geometry I
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.

Calculus and Analytic Geometry II
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.

Calculus and Analytic Geometry III
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.

Discrete Mathematics
Prereq: MATH 112 with a C or better.  Freq: Fall, Spring.
Covers 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.

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

Linear Algebra
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.

Set Theory, Logic and Proof
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.

Probability and Statistics
Prereq: MATH 221 with a grade of C or better. 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.

Advanced Probability Theory and Statistics
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.

Differential Equations and Their Applications
Prereq: MATH 222. Freq: Fall.
Examines 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.

Logic and Combinatorics
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.

Advanced Calculus
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.

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

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

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

History of Mathematics
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.

Applied Mathematics
Prereq: MATH 223, 317. 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.

Real Analysis
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.

Topics in Real Analysis
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.

Complex Analysis
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.

Abstract Algebra
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.

Topics in Abstract Algebra
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.

Topology
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.

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

Computability and Automata
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.

Special Topics in Mathematics
Prereq: Consent of instructor. Freq: Occasionally.
Intensive treatment of various specialized areas of mathematics.

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

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

Statics
Prereq: MATH 221 with grade of C or better, concurrent enrollment 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.

Dynamics
Prereq: MATH 222 with a grade of C or better, concurrent enrollment in MATH 223; PENG 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.

Electrical Circuits I
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.

Materials Science and Engineering
Prereq: CHEM 101, MATH 222, PHYS 202. Freq: Fall
Introduces materials science and engineering.  Covers the structure and basic properties of various engineering materials, including metals and alloys, ceramics, plastics, and composite materials.  Includes laboratory work.

Engineering Drawing and Computer Aided Design
Prereq: MATH 112, 113; or MATH 114. Freq: Spring.
Covers fundamentals of computer aided design (CAD), solid modeling, engineering drawings, dimensioning and specifications.

Principles of Physics
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.

College Physics I
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.

College Physics II
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.

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

Astronomy of Native America
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.

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

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

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

Modern Physics
Prereq: CHEM 101, MATH 22, PHYS 202. Freq: Fall.
Special relativity. Elements of quantum mechanics. Introduction to atomic, molecular, solid state, nuclear, and particle physics. Three-hour lecture.

Scientific Programming
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.

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

Classical Mechanics
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.

Electricity and Magnetism
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.

Computational Physics
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.

Advanced Experiments in Physics
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.

Mathematical Methods of Physics
Prereq: MATH 223, 317. Freq: Fall (even years).
Applies mathematical methods to 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.

Thermodynamics and Statistical Physics
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 thermodynamics and equilibrium statistical mechanics. Includes the laws of thermodynamics, Legendre transformations and thermodynamic potentials, Maxwell relations, thermodynamic stability and its consequences, classical and quantum statistical mechanics, and black-body radiation.

Quantum Physics
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.

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

Internship in Physics
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.

Senior Seminar
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.

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

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