Mathematics

The science of mathematics has fascinated scholars since the beginning of classical thought. The mathematics program seeks to foster in students the power of disciplined thought, an appreciation of the intrinsic beauty of mathematics, a sound understanding of mathematical concepts, and the mathematical tools required by many areas of study. As part of the general education program, all Wesleyan students must successfully complete one course from MAT 140, 150, 192, 205, or 206.

The student learning outcomes for a student majoring in mathematics are:
I. to develop an understanding of the differential and integral calculus, and their applications;
II. to have foundational knowledge of more advanced branches of mathematics such as linear algebra, differential equations, analysis, abstract algebra, and probability and statistics, and their applications;
III. to acquire knowledge of methods of mathematical proof; and
IV. to be able to use mathematical techniques to analyze and solve a variety of applied and theoretical problems.
 
Major Program: Mathematics
The mathematics major provides breadth and depth in the study of mathematics and encourages students to achieve a sound understanding of the various areas of mathematics. Students who major in mathematics have many options, including careers in industry, government, statistics, teaching, and graduate study in mathematics and engineering. Wesleyan mathematics majors have enjoyed success in these and other career options.


A student majoring in mathematics first encounters the basic ideas and methods of analysis, algebra, and geometry in the required courses of calculus, computer science, linear algebra, discrete mathematics, and physics, learning both theoretical and applied aspects of the material. She continues with courses from differential equations, abstract algebra, real analysis, and other areas, giving further breadth to her knowledge of mathematics. At the same time, she deepens her knowledge through a two-semester sequence in real analysis or abstract algebra. Finally, a capstone course based upon topics in complex variables helps her see how concepts from various branches of mathematics combine to form this cornerstone of advanced mathematics. A student begins her mathematics program at the level indicated by her background, interests, and preparation as determined by a placement examination and consultation with a member of the mathematics faculty. Internships and research are encouraged.

Major Requirements: Mathematics.
The mathematics major requires a total of 50 semester hours, including MAT 205, 206, 207, 208, 210, 230, 300, 311, 401, 405 or 419, and 415 (33 semester hours), three semester hours selected from MAT 312 or 402; eight hours of physics (PHY 121 and 122); and six hours of computer science (CSC 216 and 218.) Many students who major in mathematics begin with MAT 205 in the first semester.


A recommended sequence of courses for the student majoring in mathematics is shown below. There is some flexibility as to when the required physics sequence and the CSC courses are taken. It is advisable to take the following courses during the first two years: MAT 205, 206, 207, 208, 210, 230 or 300, and CSC 216 and 218.

Students planning to do graduate work in mathematics should take both of the sequences in real analysis and abstract algebra. Note that the sequences MAT 311, 312 and MAT 401, 402 are offered in alternate years, so such students should plan to take one of these sequences in the junior year and the other in the senior year.

Fall Spring
FIRST YEAR
MAT 205/MAT 206
WIS 101/Writing Competency Course
Elective/General Education Elective/General Education
Elective/General Education Elective/General Education
Elective/General Education Elective/General Education
 
SECOND YEAR
MAT 207/MAT 208
CSC 216/MAT 300
MAT 210/CSC 218
MAT 230/Elective/General Education
Elective/General Education Elective/General Education
 
THIRD YEAR
MAT 311 or 401 MAT 312 or 402
PHY 121 MAT 405 or 415
MAT 419 or elective PHY 122
Elective/Elective/General Education
Elective/Elective
 
FOURTH YEAR
MAT 311 or 401 MAT 312 or 402
MAT 419 or elective MAT 405 or 415
Elective/General Education Elective/General Education
Elective/General Education Elective/General Education
Elective/General Education Elective/General Education
 

Professional Development: Throughout her Wesleyan education each student is given opportunities to explore professional and career choices, and to develop and demonstrate the knowledge and skills essential for professional success. Each student will complete a PDE 400 Professional Development Experience and submit a PDE 401 Professional ePortfolio prior to graduation. To develop her understanding of how a liberal arts education enhances a student's preparation for careers and further professional growth, each student majoring in mathematics will complete an internship, or a research experience approved by the mathematics faculty.

Integrative Experience: Each student majoring in mathematics will complete a general education Integrative Experience by taking either MAT 405 or MAT 419. Both of these courses require a semester project that asks the student to make connections between her general education and the mathematics major, and to consult with a faculty member outside of mathematics on the project.

Minor Requirements: Mathematics. A minor in mathematics consists of 15 semester hours including MAT 230, 206, 210, and two other MAT courses beyond MAT 205 (not to include MAT 220) selected in consultation with the academic advisor and a member of the mathematics faculty.

Resources for Non-Majors. All Wesleyan students are welcomed and encouraged to include the study of mathematics in their coursework. The study of mathematics provides necessary skills and concepts essential in other areas of study, including natural sciences, social sciences, business, and education. The student is guided in her selection of the appropriate mathematics courses by the requirements of each discipline, her previous mathematics courses, a placement examination, and consultation with her academic advisor and a member of the mathematics faculty.

Undergraduate Research Opportunities. Independent research is a highly desirable component of the curriculum for mathematics majors. Faculty members welcome the opportunity to support and direct the research efforts of students enrolled in MAT 451, 452, and 499.

Applied Mathematical Science

Applied Mathematical Science a major program for students who are interested in mathematics, but whose interests lie primarily with the practical application of mathematics to problems in the physical sciences, life sciences, economics, engineering, and other fields, rather than in the formal areas of abstract mathematics. Applied mathematics seeks to apply existing mathematical methods across a range of practical problems, as well as to develop novel computational and predictive methods and models for specific real-world phenomena. The Applied Mathematical Science major prepares students for graduate work and careers in such diverse areas as physics, astrophysics, geology, climatology, atmospheric science, genomics, neuroscience, economics, finance, energy management, and the diverse applications of engineering. This major also specifically prepares students for admission to engineering programs under the 3-2 Dual-Degree in Engineering. (See Pre-professional programs.)

The 3-2 Dual-Degree Engineering program is a cooperative arrangement between Wesleyan and specific universities combining a Wesleyan bachelor of arts degree with a university bachelor of science degree in a nominally five-year program. Wesleyan currently has dual-degree arrangements with Mercer University, Georgia Institute of Technology, and Auburn University. Under the dual degree arrangement the student attends Wesleyan for three years and completes 90 semester hours including proficiency and general educational requirements. She will follow a closely-advised pre-engineering program of courses in mathematics and the physical sciences, and will have the option of completing a major course of study, such as Applied Mathematical Science. If the student meets the transfer entrance requirements for the cooperating university program, she then transfers to that university for approximately two years of prescribed engineering courses. At the end of this nominally five-year program, provided that the student has met both Wesleyan proficiency and general education requirements and the curricular requirements of the cooperating university, the student earns a separate baccalaureate degree from each school.

The student learning goals for students majoring in Applied Mathematical Science and/or completing the Wesleyan component of the Dual-Degree in Engineering program are:

I. to develop a sound understanding of calculus, linear algebra, and differential equations;
II. to successfully write computer programs that solve mathematical problems;
III. to build theoretical and methodological foundations in the central, quantitative, laboratory-based physical sciences;
IV. to learn to recognize phenomena that may be represented and modeled using computational, analytical, and predictive mathematical techniques; and
V. to be able to apply mathematical techniques to a diverse range of problems in the natural and social sciences.
 

Major requirements: Applied Mathematical Science: The major program requires a minimum of 50 hours of course work, including the following:

I. Required Mathematics and Computer Science Courses (21 hours):
MAT 205 Calculus I 3 hours
MAT 206 Calculus II 3 hours
MAT 207 Calculus III 3 hours
MAT 208 Calculus IV 3 hours
MAT 210 Linear Algebra 3 hours
MAT 300 Ordinary Differential Equations 3 hours
CSC 216 Programming I 3 hours
 
II. Required Natural Science Courses (16 hours):
CHM 101 General Chemistry I 4 hours
PHY 121 General Physics I 4 hours
PHY 122 General Physics II 4 hours
PHY 205 Periodic Motion and Waves 4 hours
 
III. Elective Courses (10-12 hours; at least one 300-level course):
CHM 320 Inorganic Chemistry 3 hours
CHM/PHY 361 Thermodynamics 3 hours
CHM/PHY 362 Quantum Chemistry 4 hours
ECO 202 Intermediate Macroeconomic Theory 3 hours
ECO 204 Intermediate Microeconomic Theory 3 hours
PHY 212 Modern Physics 4 hours
PHY 305 Classical Dynamics 3 hours
PHY 350 Quantum Mechanics 3 hours
*CHM 396 Special Topics in Chemistry 3 or 4 hours
*ECO 396 Special Topics in Economics 3 or 4 hours
*MAT 396 Special Topics in Mathematics 3 or 4 hours
*PHY 396 Special Topics in Physics 3 or 4 hours
*must be an approved special topics course
 
IV. Senior Capstone Course (3 hours):
MAT 405 Mathematical Modeling 3 hours
MAT 419 Probability and Statistics 3 hours
 

Recommended Course Sequence. The major in Applied Mathematical Science may be completed in four years by students lacking specific college preparatory experience in mathematics and physical science. However, students intending to complete the Dual-Degree in Engineering program within three years at Wesleyan and five years in total should arrive at Wesleyan prepared for college calculus, should consult with the Dual-Degree program advisor as soon as possible, and should plan their Wesleyan studies based on the following three-year schedule.

Recommended Course Sequence for Applied Mathematical Science:
First Year: Fall
WIS 101, MAT 205, two general education courses
First-Year: Spring
Writing Competency Course, MAT 206, three general education courses
 
Sophomore Year: Fall
MAT 207, CSC 216, PHY 121, two general education courses
Sophomore Year: Spring
MAT 208, PHY 122, two general education courses
 
Junior Year: Fall
PHY 205
MAT 210, elective/MAT 419, elective/general education, two general education courses
Junior Year: Spring
MAT 300, elective/MAT 405, elective/general education, two general education courses
 

Mathematics (MAT) Gen. Ed. Course Descriptions

140: Precalculus Mathematics.
Goal: To study, with emphasis on the function concept, the essentials of trigonometry and analytical geometry.
Content: Properties, graphs, and applications of trigonometric and inverse trigonometric functions; trigonometric identities and equations; systems of equations; conic sections; introduction to vectors, matrices, and complex numbers.
Taught: Spring.
Prerequisites: Two years of high school algebra and one year of high school geometry or the equivalent and sufficiently high score on the mathematics placement exam, or permission of the instructor, or MAT 130.
Gen. Ed. Category: Developing; Quantitative Reasoning Competency; (SM).
Credit: 3 hours.
 
150: Modeling with Algebra.
Goal: To study selected topics from college algebra and their applications
Content: Topics include the graphs and properties of linear, power, exponential, logarithmic, and polynomial functions. Applications of these functions will employ real-life data, incorporate numerical, symbolic, and geometric methods of analysis, and fit curves to the data by using least-squares criteria.
Taught: Fall.
Prerequisite: MAT 130 or equivalent.
Gen. Ed. Category: Developing; Quantitative Reasoning Competency; (SM).
Credit: 3 hours.
 
192: Introduction to Mathematical Reasoning.
Goal: To learn how to analyze and solve problems encountered in various areas of mathematics, in real life, and in other areas of study.
Content: Topics covered include problem solving, patterns in mathematics, deductive and inductive reasoning, logic, analyzing arguments, set theory, the real number system, number theory, numeration systems, graphical descriptions of data, counting methods, and basic probability and statistics.
Taught: Fall, Spring.
Prerequisite: None.
Gen. Ed. Category: Developing; Quantitative Reasoning Competency; (SM).
Credit: 3 hours.

205: Calculus I.
Goal: To study the concepts of differential calculus.
Content: Properties and graphs of algebraic and transcendental functions, limits, continuity, the derivative and some of its applications, and antiderivatives.
Taught: Fall, occasionally Spring.
Prerequisites: MAT 140 or equivalent, or two years of high school algebra, one year of high school geometry, and at least a semester of trigonometry.
Gen. Ed. Category: Developing; Quantitative Reasoning Competency; (SM).
Credit: 3 hours.

206: Calculus II.
Goal: To study the concepts of integral calculus.
Content: Riemann sums, the Fundamental Theorem of Calculus, techniques of integration, applications of the definite integral, and indeterminate forms.
Taught: Spring, occasionally Fall
Prerequisites: MAT 205 or equivalent.
Gen. Ed. Category: Developing; Quantitative Reasoning Competency; (SM).
Credit: 3 hours.

220: Statistical Methods.
Goal: To introduce students to the logic of designing an experiment and interpreting the quantitative data derived from it.
Content: A study of the binomial and normal distributions, measures of central tendency, tests of hypotheses, chi-square tests, tests for homogeneity and independence, confidence intervals, regression, and correlation.
Taught: Fall, Spring.
Prerequisite: MAT 126, 130, 140, 192, or equivalent placement.
Gen. Ed. Category: Developing; Quantitative Reasoning Competency; (SM).
Credit: 3 hours; cross-listed as PSY 220
 

Mathematics (MAT) Other Course Descriptions

130: College Algebra.
Goal: To study, with emphasis on the function concept, the essentials of algebra.
Content: General properties of graphs and functions; properties, graphs, and applications of polynomial, rational, exponential and logarithmic functions.
Taught: Fall.
Prerequisite: Two years of high school algebra and one year of high school geometry or the equivalent.
Credit: 3 hours.
 
207: Calculus III.
Goal: To expand the study of differential and integral calculus to an intermediate level.
Content: Indeterminate forms, improper integrals, sequences and infinite series, Taylor polynomials and power series, conics, polar co-ordinates, and an introduction to numerical methods and approximations.
Taught: Fall.
Prerequisites: MAT 206 or equivalent.
Credit: 3 hours.

208: Calculus IV.
Goal: To study the extension of the concepts of calculus to functions of several variables.
Content: Properties of functions of several variables, differentiation and integration in R n , vectors, parametric equations.
Taught: Spring.
Prerequisites: MAT 206 or equivalent.
Credit: 3 hours.

210: Linear Algebra.
Goal: To introduce the elements of linear algebra. To apply the theory of matrices to solve appropriate problems, including systems of linear equations.
Content: Matrices, determinants, linear systems, vector spaces, bases, linear transformations, inner products, eigenvalues, eigenvectors, and diagonalization.
Taught: Fall, occasionally Spring.
Prerequisite: MAT 205.
Credit: 3 hours.
 
230: Discrete Mathematics.
Goal: To study the basic properties of some discrete mathematical structures and to initiate the rigorous study of mathematical methods of proof.
Content: Graphs and trees, elementary number theory, including counting techniques and recursion; set theory, relations, and methods of proof, including mathematical induction and limit proofs.
Taught: Fall, occasionally Spring.
Prerequisites: MAT 206 or equivalent.
Credit: 3 hours.
 
300: Ordinary Differential Equations.
Goal: To explore methods of solving ordinary differential equations. To expand upon the techniques learned in the calculus sequence.
Content: A study of first and second order differential equations and of higher order linear differential equations, including power series methods, Laplace transform, and a brief introduction to numerical techniques.
Taught: Spring.
Prerequisites: MAT 205 and 206; 207 as a co- or prerequisite.
Credit: 3 hours.

311: Abstract Algebra I.
Goal: To study the algebraic properties of groups and rings by means of a rigorous axiomatic approach, focusing on the use of logic and on various methods of proof.
Content: A study of groups, subgroups, rings, ideals, domains, unique factorization domains, and ideal domains.
Taught: Fall. Alternate years.
Prerequisite: MAT 210 and 230.
Credit: 3 hours.

312: Abstract Algebra II.
Goal: To continue the study of algebraic properties of rings and fields. To expand understanding and use of various methods of proof. To prepare students for graduate level mathematics.
Content: A study of fields, modules, and Galois theory.
Taught: Spring. Alternate years.
Prerequisite: MAT 311.
Credit: 3 hours.

396: Special Topics in Higher Mathematics.
Goal: To provide an opportunity to examine in greater depth an area of higher mathematics.
Content: An in-depth examination of an area in advanced mathematics. The topics covered will vary. Representative special topics include graph theory, combinatorics, history of mathematics, and fractal geometry.
Taught: Offered occasionally.
Prerequisite: Permission of instructor.
Credit: 3 hours. A student may take a maximum of six to eight semester hours (two courses) of special topics in any one field.

401: Real Analysis I.
Goal: To examine more intensively topics presented in the calculus sequence, focusing on the roles of rigorous proof and logic.
Content: A study of the algebraic and topological properties of the ordered field of real numbers, sets, functions, limits, continuity, differentiation, and integration.
Taught: Fall. Alternate years.
Prerequisite: MAT 205-208 and 230.
Credit: 3 hours.

402: Real Analysis II.
Goal: To extend the concepts and techniques presented in MAT 401. To extend the calculus sequence to functions of several variables. To prepare students for graduate level mathematics.
Content: A study of the analytical properties of functions of several real variables, including differentiation, the inverse function theorem, integration, simplexes, and chains.
Taught: Spring. Alternate years.
Prerequisites: MAT 210 and 401.
Credit: 3 hours.

405: Mathematical Modeling.
Goal: To provide an opportunity for students to make connections between mathematics and other disciplines. To enable each student to analyze and adopt a particular model and to present her results in a public forum.
Content: An introduction to mathematical modeling and computer simulation of real-world phenomena, with special attention paid to the initial formulation of the model, the computer implementation of the model, and the interpretation of the mathematical or numerical results. The topics covered will include optimization models, dynamic models, and probability models while real-world phenomena will be drawn from such disciplines as biology, economics, chemistry, physics, political science, psychology, and sociology.
Taught: Spring. Alternate years.
Prerequisites: MAT 205-208, MAT 210, MAT 300, PHY 121, or permission of the instructor.
Credit: 3 hours. This course may be taken to fulfill the requirement for the senior integrative experience in Physics.

415: Complex Analysis.
Goal: To provide a capstone experience for mathematics majors and to further prepare students for graduate level study through the introduction and study of complex numbers and functions of a single complex variable.
Content: Complex numbers, complex valued functions, complex differentiation, complex integration, and properties and applications of complex analytic functions.
Taught: Spring. Alternate years.
Prerequisites: MAT 311 or 401.
Credit: 3 hours.

419: Probability and Statistics.
Goal: To study basic mathematical theory, methods, and techniques in probability and statistics, and to examine applications.
Content: A calculus-based treatment of discrete and continuous probability distributions and their applications, including the binomial, hypergeometric, Poisson, uniform, geometric, and normal distributions. Hypothesis testing and chi-square tests.
Taught: Fall. Alternate years.
Prerequisite: MAT 206.
Credit: 3 hours. This course may be taken to fulfill the requirement for the senior integrative experience in Physics.

451: Directed Independent Study.
Goal: To enable an intensive exploration of a topic of special interest. To promote original, independent, creative, and critical thinking.
Content: Directed independent work of a critical or analytical nature. Under careful faculty supervision, qualified students are encouraged to develop originality of thought and thoroughness of method. Emphasis on research methods.
Taught: Offered occasionally.
Prerequisite: Permission of program director.
Credit: 1-6 hours.

452/199: Field Study.
Goal: To provide the mathematics student with practical experience in some area.
Content: A practical experience in some area of mathematics, such as actuarial science, computer programming, or teaching. A brief plan including objectives, anticipated activities, a list of readings, and the nature of reports to be submitted to the sponsor.
Taught: Offered occasionally.
Prerequisites: Adequate background, permission of advisor, program director, faculty sponsor, and the Director of Career Development.
Credit: 1-12 hours.

499: Honors Thesis. (Fee required)
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