Mathematics Degrees

Mathematics

With a range of course offerings beginning with introductory mathematics, this department provides a strong undergraduate program. The department aims to prepare students to continue their education in graduate study; to fulfill the mathematics requirement and to provide the foundation for study in such related fields as chemistry, physics and computers; to give students the necessary background to enter certain areas of business and industry; and to acquaint students with the basic concepts of mathematics, an essential aspect of a liberal arts education. No course with a grade lower than C- will be accepted toward a major or minor in mathematics. In addition, a C average (calculated as the College calculates G.P.A.) must be maintained over all courses required for a major or a minor.
Computer Science

The computer science major is designed to give a student in this program a solid background in applied and theoretical computer science. Graduates of the program will have the skills necessary to enter the business world or pursue graduate study in computer science. The variety of computer offerings allows ample opportunity for non-majors to increase their computer skills. All undergraduates are encouraged to take as many computer courses as possible to complement their major programs. No course with a grade lower than C- will be accepted toward a major or a minor in computer science. In addition, a C average (calculated as the College calculates G.P.A.) must be maintained over all courses required for a major or minor

Major in mathematics
MATH 121, 122, 130, 231, 251, 333, 402, 421, 499; Nine hours of approved electives, selected from: (CPTR 105) MATH 233, 240, 245, 306, 330, 380 or 480, 385 or 485; (PHYS 210, 220) PHYS 301 or (CHEM 211 and PHYS 210, 220) CHEM 341; (ECON 221) ECON 350; (CPTR 205) CPTR 310. [Course Descriptions]
Three credits of a Senior Project (499) are a required part of the mathematics major.
See a planning sheet for the mathematics major.
To declare a mathematics major, students must submit an Election of Major form to the Office of the Registrar and an Entry into the Major form to the department chair of mathematics. (Entry into the Major form is available only while logged onto the MC network.)
Minor in mathematics,
MATH 121, 130; 17 hours of electives selected from: MATH 122, 231, (CPTR 105) 233, MATH 240, 245, 251, 306, 330, 333, 402, 421, 380 or 480, 385 or 485; (PHYS 210, 220) PHYS 301 or (CHEM 211 and PHYS 210, 112) CHEM 341; (CPTR 205) CPTR 310; (ECON 221) ECON 350. [Course Descriptions]
See a planning sheet for the mathematics minor.
To declare a mathematics minor, students must submit an Election of Major/Minor form to the Office of the Registrar.

100 BASIC MATHEMATICS - 2 hours
A review of topics in arithmetic and elementary algebra. Topics include: fractions, decimals, proportions and percent, signed numbers, linear equations and inequalities, and exponents. Fall.

101 MATH FOR ELEMENTARY TEACHERS I - 3 hours
A course designed especially for the teacher of elementary school mathematics. Topics include: problem solving, sets, logic, functions, numeration systems, computational algorithms, rational and irrational numbers, and number theory. Prerequisite: placement. Fall.

102 MATH FOR ELEMENTARY TEACHERS II - 3 hours
Topics include: proportional reasoning, percent, descriptive statistics, probability, intuitive geometry, transformational geometry and measurement. Prerequisite: MATH 101 or consent of instructor. Spring. GE-D.

103 SURVEY OF MATHEMATICAL THOUGHT - 3 hours
A course designed to help students learn more about the contribution of mathematics to human culture. This course develops the capacity to engage in logical thinking and to analyze and communicate technical information. Fall. Spring. GE-D.

112 COLLEGE ALGEBRA - 3 hours
Topics include: exponents and radicals, factoring, linear and quadratic equations, linear inequalities, graphs and functions, polynomials, exponential and logarithmic functions, and systems of linear equations. Prerequisite: placement. Fall. January. Spring. GE-D.

120 PRECALCULUS - 3 hours
Topics include: graphs and functions, polynomials and their zeros, complex numbers, exponential and logarithmic functions, trigonometry (functions, graphs and identities) and applications. Prerequisite: MATH 112 or placement. Fall. January. Spring. GE-D.

121 CALCULUS I - 4 hours
An introduction to calculus including limits, continuity, derivatives and their applications, curve sketching, integrals and the Fundamental Theorem of Calculus. Trigonometric, exponential and logarithmic functions are included. Graphing calculators will be used. Prerequisite: MATH 120 or placement. Fall. Spring. GE-D.

122 CALCULUS II - 4 hours
Topics include: numerical integration, applications of integration, techniques of integration, inverse trigonometric functions, an introduction to differential equations, improper integrals, sequences and series and Taylor’s Theorem. A computer-algebra system will be used. Prerequisite: MATH 121. Fall. Spring.

130 DISCRETE MATHEMATICS - 4 hours
An introduction to discrete methods used in mathematics and computer science. Principal topics covered are: logic, sets, algorithms, number theory, reasoning and proof, recursion, combinatorics, relations and graph theory. Prerequisite: MATH 120 or consent of the instructor. Spring. GE-D

210 INTRODUCTION TO STATISTICS - 4 hours
An introduction to common statistical techniques used in business, social sciences and natural sciences. Course includes: graphic representation of data; sampling design; elementary probability; discrete and continuous random variables; binomial, uniform, normal, student’s t, and chi-squared distributions; linear regression; techniques for estimating and testing population means and proportions; and introduction to non-parametric tests. Students are introduced to a statistical software package during weekly lab sessions. As significant computer work is required, students are expected to possess computer skills comparable to CPTR 101 (i.e., familiarity with the campus network, the web, Windows and Windows applications.) Students are encouraged to take college algebra or have equivalent skills prior to enrolling. Fall. January. Spring. GE-D.

231 MULTIVARIABLE CALCULUS - 4 hours
Topics include: vector analysis in two-and three-dimensional spaces, polar and spherical coordinates, curves in space; multivariable functions and their derivatives, multiple integrals, line integrals, and Green’s and Stokes’ Theorems. Prerequisites: MATH 122, 251. Spring.

233 NUMERICAL ANALYSIS - 3 hours
A study of computational issues and methods used in applied mathematics and scientific computing. Topics include: computation errors; interpolation; convergence of numerical methods; approximate integration; numerical solution of ordinary differential equations; and numerical solution to systems of linear and non-linear equations. The course is oriented toward machine computation and involves programming of various solution techniques. Prerequisite: CPTR 105; MATH 121. Spring, odd years

Mathematics is a field of increasing importance to society and technology. At Manchester, students can prepare for a career in education, research, or applied mathematics. The student who chooses a mathematics major will have the background to apply mathematics to problems in the natural and social sciences and in business and industry.
Entering students take a placement test in mathematics as part of new student orientation. The test results in conjunction with other criteria are used to place students in an appropriate beginning mathematics course. Advanced placement credit in calculus is possible for students who have an especially strong background in mathematics.
Check out brochures describing our students’ success in mathematics and secondary education.

General Education Requirements
Thirty-six (36) hours of General Education courses must be selected from the five areas of the Associate in Arts Degree General Education Requirements as listed on General Education Requirements Page, including CGS 1000-Computer Information Systems and HLP 1081-Concepts of Wellness.
Discipline Prerequisites
Course Description Semester Hours
EDF 1005 Introduction to Education + Field Experience 3
EDG 2701 Teaching Diverse Populations + Field Experience 3
EME 2040 Introduction to Educational Technology 3
BSC 1006C General Biology II or
BSC 2010C Fundamentals of Biology I or
BSC 2011C Fundamentals of Biology II 4
MAC 2311 Calculus with Analytic Geometry I 4
COP 1000 Fundamentals of Computing with C++ 3
Electives (Mathematics or Physical Science courses) 4

General Education Requirements Thirty-six (36) hours of General Education courses must be selected from the five areas as listed, including CGS 1000-Computer Information Systems, HLP 1081-Concepts of Wellness and SPC 1600-Fundamentals of Speech Communication.
Discipline Prerequisites
Course Description Semester Hours
COP 1000 Fundamentals of Computing with C++ 3
MAC 2311-2312-2313 Calculus with Analytic Geometry I, II, III 12
CHM 2045C-2046C General Chemistry I, II 8
PHY 2048C-2049C General Physics with Calculus I, II 8
Subtotal 3

General Education Requirements

Thirty-six (36) hours of General Education courses must be selected from the five areas of the Associate in Arts Degree General Education Requirements as listed on General Education Requirements Page, including CGS 1000-Computer Information Systems and HLP 1081-Concepts of Wellness.
Discipline Prerequisites
Course Description Semester Hours
EDF 1005 Introduction to Education + Field Experience 3
EDG 2701 Teaching Diverse Populations + Field Experience 3
EME 2040 Introduction to Educational Technology 3
MAC 2311-2312 Calculus with Analytic Geometry I, II 8
COP 1000 Fundamentals of Computing with C++ 3
Electives (Mathematics courses) 4
Subtotal 24

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240 MATHEMATICAL STATISTICS - 4 hours
Basic concepts of probability; expectation; variance, covariance, distribution functions; bivariate, marginal and conditional distributions. Treatment of experimental data; normal sampling theory; confidence intervals and test of hypotheses; introduction to regression and to analysis of variance. Prerequisite: MATH 122. Fall, odd years.

245 ORDINARY DIFFERENTIAL EQUATIONS - 3 hours
Topics include: classification of differential equations; methods of solving first order equations, second and higher order linear equations, and systems of linear equations; series solutions; and existence theorems. Prerequisite: MATH 122. Spring, even years.

251 LINEAR ALGEBRA I - 4 hours
Solution of linear systems, matrices and determinants, eigenvalues and eigenvectors, vector algebra, representation of lines and planes in Rn, linear transformations and mathematical models using matrix algebra. Prerequisites MATH 121, 130; or consent of the instructor. Fall.

303 MATH FOR ELEMENTARY TEACHERS III - 3 hours
The study of curriculum, methods, computer applications, materials and assessment for elementary school mathematics programs. Taken as part of the Elementary Methods Block, with field experiences a required component. Prerequisites: MATH 101, 102. Fall.

306 GEOMETRY - 3 hours
A study of the logical structure and content of both Euclidean and non-Euclidean geometries. The approach to Euclidean geometry is via Hilbert’s axioms. Prerequisite: MATH 251. Fall, even years.

330 OPERATIONS RESEARCH MODELS - 3 hours
Introduction to mathematical modeling processes; allocation models involving linear programming; simplex algorithm; dynamic programming; transportation models; network models; graph theory; Markov chain models; queuing theory and game theory. Prerequisite: MATH 130 or 251 or consent of instructor. January or spring, even years.

333 ALGEBRAIC STRUCTURES - 4 hours
Basic properties of groups, rings, factor groups, ideals, quotient rings, integral domains, fields, polynomials and elementary number theory. Prerequisite: MATH 251. Fall, odd years.

402 LINEAR ALGEBRA II - 3 hours
Numerical methods for solving linear systems, the four fundamental subspaces and applications, orthogonality and approximation, eigenvectors, eigenvalues, and diagonalization of matrices and applications. Prerequisite: MATH 251. Spring, odd years.

421 REAL ANALYSIS - 3 hours
Topics include: the completeness of the real number system; sequences and their limits; elementary point-set topology; and continuity and uniform continuity. The theory of series, the derivative and the Riemann integral will be treated as time permits. Prerequisites: MATH 130, 231. Fall, even years.

475 INTERNSHIP IN MATHEMATICS - 1-3 hours
Students work in business, industry, government or other agencies applying mathematical tools (e.g., probability, statistics, optimization) to real-world problems. Students are supervised by a professional with significant experience in such applications and also a faculty member. A written report describing the overall project and the student’s contribution will complete the course. Students must formally enroll in this course prior to beginning their work experience. Course may be repeated once for a maximum of four hours credit. Prerequisite: MATH 130, 122; permission of the department chair.

499 SENIOR PROJECT (W) - 1-3 hours
An in-depth study of some area of mathematics under the guidance of a primary and secondary faculty advisor. Students will write a thesis and give an oral presentation based on the thesis. Students will enroll either once or twice for a total of three hours credit. Prerequisite: ENG 111; permission of the department chair.

380 or 480 SPECIAL PROBLEMS - 1-4 hours
A student who has demonstrated ability to work independently may propose a course and pursue it with a qualified and willing professor. The department chair and the vice president and dean for academic affairs must also approve. A set of guidelines is available at the Office of the Registrar.

385 or 485 SEMINAR - 1-4 hours
An in-depth consideration of a significant scholarly problem or issue. Students pursue a supervised, independent inquiry on an aspect of the topic and exchange results through reports and discussions

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