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Mathematics: Requirements and Courses

Mathematics
 2009-2010 Faculty: Dr. Chris Morin, Dr. Edward Boamah, Mr. Bishop, Mr. Genta, Dr. M. Meredith
Requirements
 
Requirements for a Mathematics Major
MA 215, 240, 254, 255, 256; 303, 341, 350, 351, 401, MA 490; plus nine additional hours chosen from MA 300 (no more than 3 hours), 308, 310, 311, or 315; CS 211, 212; CH 101-102 or PH 201-202.
 
TOTAL: 38 semester hours in mathematics plus 16 outside the department.
 
Requirements for a Mathematics Minor
MA 240; 254, 255, 256; 303 or 341, plus six additional hours of mathematics above MA 300.

TOTAL: 21 semester hours.
 
Requirements for a Secondary Mathematics Education Major
MA 215, 240, 254, 255, 256, 303, 308, 341, 350, 351, 401, 490; CS 211, 212; six additional hours from the following: MA 300 (no more than 3 hours), 310, 311, or 315; ED 100, 120, 200, 220, 240, 315, 320, 328, 370, 400, 410, 491, 492. (Additional course work may be required for Illinois State certification.)

TOTAL: 47 semester hours plus 48 semester hours of professional education courses required for certification.  If middle school endorsement is desired, candidate must complete PY 227 and ED 304.
 

Courses

 100. Intermediate Algebra (3 hours)
Each Semester. 
Study of real numbers, linear and quadratic equations, exponents, polynomials, factoring, rational expressions, radicals, graphing, systems of equations and functions. Students’ placement will be determined by high school mathematics achievement, ACT/SAT results, and/or diagnostic tests. Students must achieve a ‘C’ or better in order to proceed onto further mathematics course work at the College.

120. Liberal Arts Mathematics (3 hours)
Each Semester 
Seeks to broaden students’ understanding of the discipline of mathematics by surveying topics chosen from algebra, geometry, and discrete mathematics. Intended for non-majors. Topics may include sets, logic, probability, matrices, numerical systems, and applications.
Prerequisite: departmental placement, permission, or MA 100.

140. Precalculus (3 hours)
Each Semester. 
Topics include equations and inequalities, functions and graphs, polynomial, rational, exponential, logarithmic, and trig functions, laws of Sines and Cosines, polar coordinates, complex numbers, systems of equations and inequalities, matrices, determinants, and sequences and series.
Prerequisite: Placement test or permission.

215. An Introduction to Mathematical Software (1 hour)
First Semester. 
An introduction to some mathematical software and their applications to different fields of mathematics such as algebra, calculus, discrete mathematics, geometry, group theory, linear algebra, number theory, operations research, and statistics.
Prerequisite: MA 254.

220. Mathematics for Elementary School Teachers I (3 hours)
First Semester. 
The study of concepts underlying elementary mathematics. Topics include 1) problem solving, 2) sets, functions, and reasoning, 3) whole numbers, 4) number theory, 5) integers and fractions and 6) rational and irrational numbers. Elementary Education majors only. Must also complete MA 221.

221. Mathematics for Elementary School Teachers II (3 hours)
Second Semester. 
The study of concepts underlying elementary mathematics. Topics include 1) statistics, 2) probability, 3) geometry, 4) measurement, 5) motions in geometry, 6) algebra and algebraic thinking. Elementary Education majors only.
Prerequisite: MA 220.

240. Discrete Mathematics (3 hours)
First Semester. 
Introduction to concepts of discrete mathematics prerequisite to an understanding of advanced mathematics and computer science. Topics include set theory, functions, relations, mathematical logic, propositional and predicate calculus, proof techniques, concepts of probability, Boolean algebra, and an introduction to graph theory.
Prerequisites: MA 140; CS 211 or concurrent registration; and sophomore standing. (IAI: M1 905)

254. Calculus I (3 hours)
Each Semester. 
The basic concepts, techniques, and applications of differentiation and integration of functions of a real variable. Topics include limits, continuity, differentiability, integration, and the Fundamental Theorem of Calculus.
Prerequisite: MA 140 or placement. (IAI: M1 900-1)

255. Calculus II (3 hours)
Second Semester.
A continuation of MA 254. Topics include the transcendental functions, methods of integration and series. Prerequisite: MA 254. (IAI: M1 900-2)

256. Calculus III (3 hours)
First Semester. 
An extension of calculus to functions of several variables. Topics include vectors, partial differentiation, multiple integration, line and surface integrals.
Prerequisite: MA 255. (IAI: M1 900-3)

300. Internship (1-12 hours)
Each Semester. 
Internships involve working and learning experiences off campus. Each student’s progress is developed according to established College guidelines under the sponsorship of a faculty member. See the Index under “Internships” for reference to additional information on internship guidelines, or consult the department chair.
Prerequisite: Junior standing or above. Not open to any student who is on academic, disciplinary, or Work Program probation.

301. Calculus Based Physics (1 hour)
Second Semester. 
The theory and application of calculus to physics is studied as a supplement to the non-calculus, college physics sequence. This is intended for those students who want a more rigorous mathematical treatment of the subject or who require a calculus based physics course to enter an engineering or graduate program.
Prerequisites: MA 256, PH 201.

303. Abstract Algebra (3 hours)
Second Semester. 
Concepts of sets, mappings, and abstract structures, including an introduction to the theory of groups, rings, fields, integral domains and polynomials over a ring.
Prerequisite: MA 240.

308. Probability and Statistics (3 hours)
Second Semester, alternate years. Offered 2011-2012. 
Topics include probability, theory of statistical inference, estimation, and distribution using techniques from calculus.
Prerequisite: MA 256.

310. Computational Mathematics (3 hours)
First Semester, alternate years. Offered 2011-2012. 
A study of selected areas involving a blend of mathematical and computational approaches. Topics may include fractal geometry, graph theory, modeling and simulation, or numerical analysis. May be repeated with permission.
Prerequisites: CS 212, MA 255.

311. Differential Equations (3 hours)
First Semester, alternate years. Offered 2010-2011. 
Solution of first order differential equations, linear differential equations, power series solutions, and some special functions of mathematical physics.
Prerequisite: MA 256.

315. Operations Research (3 hours)
Second Semester, alternate years. Offered 2010-2011. 
Introduction to Operations Research. Topics of study will include the simplex method, duality theory and sensitivity analysis, transportation and assignment problems, and network optimization models. Prerequisites: MA 240, 254.

341. Linear Algebra (3 hours)
Second Semester. 
Topics include coordinate geometry, solving systems of equations, matrices and determinants, matrix algebra, vector spaces, and linear transformations.
Prerequisite: MA 240.

350. Analysis I (3 hours)
First Semester. 
An extension of calculus of one real variable to complex functions. Topics include algebra of complex numbers, elementary complex functions, analytic functions, contour integrals, and series representations for analytic functions.
Prerequisites: MA 256 and MA 303 or 341.

351. Analysis II (3 hours)
Second Semester. 
Includes a rigorous treatment, and generalizations, of material covered in MA 254. Topics include the topology of the real line and Euclidean space, sequences, series, compact sets, continuous functions, differentiation, and integration.
Prerequisite: MA 350.

399. Independent Study (1-3 hours)
Each Semester.  
Independent approved study under guidance of the department culminating in an oral and/or written presentation. May be repeated for a maximum of six semester hours.
Prerequisites: Junior standing and consent of the instructor.

401. Topics in Geometry and Topology (3 hours)
First Semester. 
The study of selected topics in geometry and topology, depending upon demand and staff.
Prerequisite: MA 351.

490. Seminar in Mathematics (1 hour)
Second Semester. 
Student presentations from the mathematical literature to develop skill in reading and presenting mathematics. Class discussions of various problems designed to improve problem solving ability, and introduce the student to the techniques of mathematical research.
Prerequisite: Junior standing, mathematics major.