Mathematics
Dr. Janet McShane
Chair of the Department
The Department of Mathematics plays a vital role in the education of all students at Manhattan College through its offerings of programs for our majors as well as for the many support courses it offers for other departments across the college. We provide students the mathematical skills necessary to be successful in their field of study whether it is mathematics, science, engineering, business, education or the liberal arts.
The mathematics curriculum for our majors allows students to prepare for careers in business, industry, actuarial science and teaching as well as to prepare for the study of mathematics at the graduate level. Yearlong courses in Linear Algebra, Abstract Algebra, and Analysis prepare students for further work in pure or applied mathematics. A selection of courses from Linear Algebra, Probability, Statistics, and Operation Research form the basis for work in finance, engineering, and all of the sciences. Students may select from a variety of advanced topics offered by faculty with expertise in an area of pure or applied mathematics.
Our classes are small which gives students the opportunity to build strong relationships with faculty. Students are invited to participate in national mathematics competitions such as the Putnam Exam and the Mathematical Modeling Contest. Many students participate in undergraduate research projects; funds, both internally and externally, are available to support these projects during the summer. Students are encouraged to present their work at the Spuyten Duyvil Undergraduate Mathematics Conference, which was founded by the Mathematics Department at Manhattan College, as well as at other national and regional meetings.
Any student wishing to participate in the Study Abroad program will find the Department makes every effort to provide the needed support to allow them to finish their required course work.
The Department is a member of the national mathematics honor society, Pi Mu Epsilon, which is dedicated to the promotion of mathematics and recognition of students who successfully pursue mathematical understanding. Students are nominated for membership in this honor society. The Department also nominates students who make presentations at conferences for membership in Sigma Xi, an international honor society for science and engineering.
Degree Plans
The Department of Mathematics offers the following programs:
- Major in Mathematics
- Bachelor of Science Degree
- Bachelor of Arts Degree
- Second Major in Mathematics
- Concentration in Applied Mathematics
- Minor in Mathematics
Also, the Department works closely with the School of Education & Health on the requirements for the BS in Adolescence Education Mathematics which prepares students to teach at the secondary level and the Mathematics emphasis in the BS in Childhood Education which prepares students to teach at the elementary level. The requirements for the BS in Adolescence Education Mathematics are listed below under second major in mathematics.
General Requirements
Courses should be taken in accordance with the Plans of Study listed below. The order in which core courses are taken is flexible but care should be taken in planning your program since some courses are not offered every semester. A minimum grade of C is required in each of the courses used for any of the listed programs (major, second major, concentration, or minor).
Major in Mathematics
BS in Mathematics
MATH 185 | Calculus I ^{*} | 3 |
MATH 186 | Calculus II ^{*} | 3 |
MATH 243 | Discrete Foundations | 3 |
MATH 272 | Linear Algebra I | 3 |
MATH 285 | Calculus III ^{*} | 3 |
MATH 331 | Probability | 3 |
MATH 336 | Applied Statistics | 3 |
MATH 377 | Algebra I | 3 |
MATH 387 | Analysis I | 3 |
MATH 471 | Linear Algebra II | 3 |
MATH 478 | Algebra II | 3 |
MATH 489 | Problem Seminar | 3 |
MATH 490 | Complex Analysis | 3 |
Math Electives | 6 | |
CMPT 101 | Computer Science I | 3 |
MATH 158 | Introduction to Mathematical Computation | 3 |
PHYS 101 & PHYS 191 | Physics I and Physics I Lab | 4 |
PHYS 102 & PHYS 192 | Physics II and Physics II Laboratory | 4 |
Natural Sciences | 8 | |
Total Credits | 67 |
* | Students who major in mathematics and are selected for the honors sequence will be enrolled in the Honors sections of Calculus I, II, and III (MATH 187, 188, and 287). |
BA in Mathematics
MATH 185 | Calculus I ^{*} | 3 |
MATH 186 | Calculus II ^{*} | 3 |
MATH 243 | Discrete Foundations | 3 |
MATH 272 | Linear Algebra I | 3 |
MATH 285 | Calculus III ^{*} | 3 |
MATH 331 | Probability | 3 |
MATH 336 | Applied Statistics | 3 |
MATH 377 | Algebra I | 3 |
MATH 387 | Analysis I | 3 |
MATH 471 | Linear Algebra II | 3 |
MATH 478 | Algebra II | 3 |
MATH 489 | Problem Seminar | 3 |
MATH 490 | Complex Analysis | 3 |
Math Electives | 6 | |
CMPT 101 | Computer Science I | 3 |
MATH 158 | Introduction to Mathematical Computation | 3 |
3 SCI Courses ^{**} | 9 | |
Total Credits | 60 |
* | Students who major in mathematics and are selected for the honors sequence will be enrolled in the Honors sections of Calculus I, II, and III (MATH 187, 188, and 287). |
** | Students may opt for one full year of a lab science (8 credits). In this case, the student will graduate with 120 credits. Students may also opt to replace the 3 SCI XXX courses with 9 credits of courses within a single discipline in the School of Science. |
Second Major in Mathematics
Students from the Schools of Liberal Arts, Business, Engineering, and Science
To complete a second major in Mathematics, students from the above Schools will need to take a total of 36 credits of mathematics courses from the mathematics major courses listed above. These credits must include MATH 185, 186, 243, 272, 377, and 387, and at least 2 courses at the 400 level.
Students from the School of Education & Health
Students pursuing a degree in Adolescence Education Mathematics earn a second major in mathematics by completing the following sequence as required by their degree program.
BS in Adolescence Education Mathematics
MATH 185 | Calculus I | 3 |
MATH 186 | Calculus II | 3 |
MATH 243 | Discrete Foundations | 3 |
MATH 272 | Linear Algebra I | 3 |
MATH 285 | Calculus III | 3 |
MATH 331 | Probability | 3 |
MATH 336 | Applied Statistics | 3 |
MATH 361 | Introduction to Higher Geometry | 3 |
MATH 377 | Algebra I | 3 |
MATH 387 | Analysis I | 3 |
MATH 489 | Problem Seminar | 3 |
MATH 422 | Seminar for Mathematics Education | 3 |
CMPT 101 | Computer Science I | 3 |
MATH 158 | Introduction to Mathematical Computation | 3 |
CMPT 214 | Teaching and Learning with Technology | 3 |
Total Credits | 45 |
* | Sequencing of courses is very important so that only one course (MATH 422) is required during the semester when the student is doing student teaching. |
Concentration in Applied Mathematics
The 24 credit hour Concentration in Applied Mathematics is designed to complement major study in a different discipline, and prepare students to use mathematics in the workplace. The concentration offers more depth than the minor in Mathematics and is currently approved for students in most majors in the Schools of Arts, Business, Engineering, and Science.
The requirements are flexible. There is a 12 credit hour required core which includes Calculus I-II-III (MATH 185, 186, 285) and Linear Algebra (MATH 272). Students choose the remaining 12 credits from a list of approved courses, including Differential Equations (MATH 286), Probability (MATH 331), Partial Differential Equations (MATH 386), Vector Calculus (MATH 385), Statistical Inference (MATH 432), Machine Learning (MATH 457), Operations Research (MATH 455), Linear Algebra II (MATH 471), and Topics in Mathematics. Students must select at least one two-term sequence for depth.
Completion of the Concentration will be documented on the student's transcript.
Minor in Mathematics
The minor in Mathematics consists of a minimum of 15 credits and must include a yearlong calculus sequence. The eligible courses vary depending on the student’s major. Specific requirements are listed below. A grade of at least a C is required for all courses meeting the requirements for a minor in Mathematics.
Note: The following courses may not be used toward the Mathematics minor: MATH 100, 111, 151, 153, 158, 221, 222, 230, 320, 321, 322 and 422.
Application: To pursue the minor in Mathematics, a student must get a Minor Form from the department, fill it out, and have it signed by the Chair of the Department of Mathematics. An approved form will be forwarded to the appropriate dean.
Minor Requirements for Students in the School of Science
The minor in Mathematics consists of a minimum of 15 credits including Calculus I (MATH 155 or 185), Calculus II (MATH 156 or 186), and Calculus III (MATH 285). The remaining courses should be chosen from the list of courses required for the mathematics major, and selected 300-400 level courses, including Topics courses, with approval of the Department Chair.
Minor Requirements for Students in the School of Engineering
The minor in Mathematics consists of a minimum of 15 credits including MATH 185, 186, 285, and 286. The remaining course(s) can be chosen from the following: MATH 243, 272, 331 (not approved for EECE and CE), 385 (not approved for EECE), 386, 432 (not approved for EECE or CE), 455, 490 (recommended for EECE), selected 300-400 level courses, including Topics courses, with approval of the Department Chair.
Minor Requirements for Students in the School of Liberal Arts or School of Business
The minor in mathematics consists of a minimum of 15 credits including Calculus I (MATH 154 or 155 or 185) and Calculus II (MATH 156 or 186). The remaining courses can be chosen from the following: MATH 243, 272, 285, 286, 331, 385, 386, 432, 455, 490, and selected 300-400 level courses, including Topics courses, with approval of the Department Chair.
BS in Childhood Education - Mathematics Plans
All students majoring in Childhood Education take the following 6 credit core sequence.
MATH 221 | Mathematics for the Elementary School Teachers I | 3 |
MATH 222 | Mathematics for the Elementary School Teachers II | 3 |
In addition, students majoring in Childhood Education may choose to do either a Concentration in Mathematics or an Emphasis in Mathematics as detailed below.
BS in Childhood Education – Mathematics Concentration
Childhood Education majors may choose to concentrate in Mathematics. These students take 30 credits in Mathematics including MATH 185, MATH 186, MATH 243, MATH 272, MATH 285, MATH 331, MATH 361, MATH 422, MATH 432 plus one additional elective approved by the Mathematics Department.
BS in Childhood Education – General Studies Concentration with Mathematics
Childhood Education majors may choose a General Studies Concentration with Mathematics as one area. These students take 15 credits in Mathematics. Please see the Department of Mathematics or the Department of Education for the requirements for this option.
PLAN OF STUDY
Bachelor of Science in Mathematics
First Year | |||
---|---|---|---|
Fall | Credits | Spring | Credits |
MATH 185 | 3 | MATH 186 | 3 |
CMPT 101 | 3 | MATH 158 | 3 |
MFL^{*} | 3 | MFL^{*} | 3 |
ENGL 110 | 3 | RELS 110 | 3 |
LLRN 102 | 3 | Social Science | 3 |
SCI 100 | 1 | ||
16 | 15 | ||
Second Year | |||
Fall | Credits | Spring | Credits |
MATH 285 | 3 | MATH 272 | 3 |
MATH 243 | 3 | MATH 336 | 3 |
PHYS 101 & PHYS 191 | 4 | PHYS 102 & PHYS 192 | 4 |
PHIL 150 | 3 | ENGL 150 | 3 |
Social Science | 3 | Free Elective | 3 |
16 | 16 | ||
Third Year | |||
Fall | Credits | Spring | Credits |
MATH 331^{***} | 3 | MATH 387 | 3 |
MATH 377 | 3 | MATH 478 | 3 |
MATH 471 | 3 | RELS 2XX Catholic Studies | 3 |
Natural Science^{**} | 4 | Natural Science^{**} | 4 |
HIST 150 | 3 | MUSC 150 or ART 150 | 3 |
16 | 16 | ||
Fourth Year | |||
Fall | Credits | Spring | Credits |
MATH 489 | 3 | MATH 490 | 3 |
MATH Elective | 3 | MATH Elective | 3 |
Free Electives | 9 | Free Electives | 6 |
RELS 3XX Global/Contemporary | 3 | ||
15 | 15 | ||
Total Credits: 125 |
* | One year sequence of a Modern Foreign Language. |
** | One year (8 credits with lab) of the same natural science is required. |
*** | If MATH 432 Statistical Inference is taken as a Math elective, it is recommended it be taken immediately following MATH 331 Probability. |
Bachelor of Arts in Mathematics
First Year | |||
---|---|---|---|
Fall | Credits | Spring | Credits |
MATH 185 | 3 | MATH 186 | 3 |
CMPT 101 | 3 | MATH 158 | 3 |
MFL^{*} | 3 | MFL^{*} | 3 |
ENGL 110 | 3 | RELS 110 | 3 |
LLRN 102 | 3 | Social Science | 3 |
SCI 100 | 1 | ||
16 | 15 | ||
Second Year | |||
Fall | Credits | Spring | Credits |
MATH 285 | 3 | MATH 272 | 3 |
MATH 243 | 3 | MATH 336 | 3 |
SCI XXX^{**} | 3 | SCI XXX | 3 |
PHIL 150 | 3 | SCI XXX | 3 |
Social Science | 3 | ENGL 150 | 3 |
15 | 15 | ||
Third Year | |||
Fall | Credits | Spring | Credits |
MATH 331^{***} | 3 | MATH 387 | 3 |
MATH 377 | 3 | MATH 478 | 3 |
MATH 471 | 3 | RELS 2XX Catholic Studies | 3 |
HIST 150 | 3 | MUSC 150 or ART 150 | 3 |
Free Elective | 3 | Free Elective | 3 |
15 | 15 | ||
Fourth Year | |||
Fall | Credits | Spring | Credits |
MATH 489 | 3 | MATH 490 | 3 |
MATH Elective | 3 | MATH Elective | 3 |
Free Electives | 9 | RELS 3XX Global/Contemporary | 3 |
Free Electives | 6 | ||
15 | 15 | ||
Total Credits: 121 |
* | One year sequence of a Modern Foreign Language. |
** | Students may opt for one full year of a lab science (8 credits). In this case, the student will graduate with 120 credits. Students may also opt to replace SCI XXX with 9 credits of courses from within a single discipline in the School of Science. |
*** | If MATH 432 Statistical Inference is taken as a Math elective, it is recommended it be taken immediately following MATH 331 Probability. |
Courses
MATH 096. Bridge Course for Business. 0 Credits.
This online course is intended for incoming Business students identified by the Mathematics placement exam. (Linear Analysis for Business). It includes a review of the fundamentals of algebra, functions and their graphs, logarithmic and exponential functions, Excel spreadsheets.
MATH 099. Bridge Course For Science/Engi. 0 Credits.
Algebra basics, lines and distance, functions and their graphs, polynomial and rational functions, exponential and logarithmic functions, trigonometry. Intended for student in science and engineering with marginal non-passing TRAM scores. The student must obtain a C or better to be placed in Calculus I in the fall.
MATH 100. Pre-Calculus Mathematics. 3 Credits.
Basic set theory, functions, and their graphs. Topics from algebra, theory of equations, trigonometry and analytic geometry. Intended to prepare students for a course in calculus. Meets four hours per week.
MATH 111. Pre-Calculus for Business Students. 3 Credits.
Review of elementary algebra, introduction to analytic geometry, functions and their graphs, logarithmic and exponential functions, polynomial functions. Meets four hours per week.
MATH 151. Topics in Modern Math. 3 Credits.
An introduction to a mathematical topic of particular interest to students in the humanities or social sciences. Possibilities include but are not limited to the mathematics of social choice, mathematics and art, mathematics and music, modeling for environmental issues, network theory, consumer mathematics. Descriptions of particular topic chosen will be available at the time of offering.
MATH 153. Linear Mathematical Analysis. 3 Credits.
Survey of business applications. Topics include financial mathematics: simple and compound interest, annuities and amortization of loans; linear optimization: solving systems of linear equations and matrix algebra; probability: elementary counting techniques, odds, and expected value. Prerequisite: A satisfactory score on the mathematics placement exam or C or better in MATH 111.
MATH 154. Calculus for Business Decisions. 3 Credits.
A one-semester course in the calculus of functions of one variable, intended for students in Business. Polynomial, rational, and exponential and logarithm functions. Limits, derivatives, techniques and applications of differentiation. Indefinite and definite integrals, applications of the integral. Prerequisite: A satisfactory score on the mathematics placement exam or a C or better in MATH 111.
MATH 155. Calculus for the Life Sciences I. 3 Credits.
Limits, continuity, exponential/logarithmic functions differentiation/antidifferentiation. An introduction to the definite integral. Meets four hours per week. Prerequisite: A satisfactory score on the mathematics placement exam or a C or better in MATH 100.
MATH 156. Calculus for the Life Sciences II. 3 Credits.
Applications chosen from the life sciences, including population, decay, growth models, stability, and matrix methods. Volumes of solids, integration techniques, difference/differential equations. Meets four hours per week. Prerequisite: MATH 155.
MATH 158. Introduction to Mathematical Computation. 3 Credits.
Introduction to mathematical problem-solving employing modern software used for mathematical modeling in industry and research. Numerical and symbolic computation including problems from calculus. Variety of problems arising in mathematics, science, and engineering. Prerequisite: CMPT 101 Co-requisite: MATH 186.
MATH 185. Calculus I. 3 Credits.
Limits, transcendental functions, continuity, derivatives and their applications, an introduction to the definite integral, and the Fundamental Theorem of Calculus. Meets four hours per week. Prerequisite: A satisfactory score on the mathematics placement exam or a C or better in MATH 100.
MATH 186. Calculus II. 3 Credits.
Applications of the definite integral, integration techniques, improper integrals, and infinite sequences and series. Meets four hours per week. Prerequisite: A grade of C or better in Calculus I (MATH 155 or MATH 185 or MATH 187).
MATH 187. Honors Calculus I. 3 Credits.
Rigorous development of differential and integral calculus. Restricted to select students who will take this courses in lieu of MATH 185. Meets four hours per week. Prerequisite: Students will be selected by the professor.
MATH 188. Honors Calculus II. 3 Credits.
Rigorous development of differential and integral calculus. Restricted to select students who will take this courses in lieu of MATH 186. Meets four hours per week. Prerequisite: Students will be selected by the professor.
MATH 221. Mathematics for the Elementary School Teachers I. 3 Credits.
Courses for prospective teachers in elementary school who are not majoring in mathematics. The content and method will follow the current standards of the National Council of Teachers of Mathematics for the elementary level. Topics include tools for problem solving, numeration systems, number theory, and algebra.
MATH 222. Mathematics for the Elementary School Teachers II. 3 Credits.
Courses for prospective teachers in elementary school who are not majoring in mathematics. The content and method will follow the current standards of the National Council of Teachers of Mathematics for the elementary level. Topics include tools for problem solving, geometry, measurement, and statistics. Prerequisite: MATH 221.
MATH 230. Elementary Statistics. 3 Credits.
An introduction to statistical methods: descriptive statistics, association between two variables, basic probability, discrete random variables, binomial and normal random variables, sampling distribution, confidence intervals, tests of significance.
MATH 243. Discrete Foundations. 3 Credits.
An introduction to the mathematical concepts and techniques of discrete mathematics: Topics include principles of logical argument, modular arithmetic and congruence classes, induction, sets, functions, relations, summations, the binomial theorem cardinality of sets. Topics form the mathematical basis of computer science and are pivotal to the study of advanced mathematics. Prerequisite: A grade of C or better in Calculus II (MATH 156, MATH 186, or MATH 188) or a C or better in MATH 185 and current enrollment in MATH 186.
MATH 244. Discrete Mathematics II. 3 Credits.
A continuation of MATH 243. Principles of counting, permutations and combinations, discrete probability, inclusion -exclusion, combinatorial arguments, graphs, matrices, isomorphism, markov chains, graph properties, trees, search trees, weighted trees, introduction to analysis of algorithms. Prerequisite: MATH 243.
MATH 272. Linear Algebra I. 3 Credits.
Linear equations and matrices, vector spaces, subspaces, linear independence, bases, dimension, inner product spaces, linear transformations, eigenvalues and eigenvectors, orthogonal matrices and diagonalization. Prerequisite: MATH 243 or MATH 285.
MATH 285. Calculus III. 3 Credits.
Algebraic and geometric aspects of vectors, functions of several variables, partial derivatives, multiple integrals, vector calculus, line integrals, Green’s Theorem. Prerequisite: A grade of C or better in Calculus II (MATH 155, MATH 186, or MATH 188).
MATH 286. Differential Equations. 3 Credits.
This course focuses on techniques of solving first-order, second-order, and systems of first-order ordinary differential equations. Methods include separation of variables, variation of parameters, and the Laplace transform. Applications include linear and nonlinear models. Prerequisite: Calculus III (MATH 285 or MATH 287).
MATH 287. Honors Calculus III. 3 Credits.
Honors equivalent to Calculus III. Algebraic and geometric aspects of vectors, functions of several variables, partial derivatives, multiple integrals, vector calculus, line integrals, Green’s Theorem. Intended for students who have completed the honors section of Calculus II (MATH 188). Prerequisite: MATH 188 or permission of instructor.
MATH 320. Fundamental Concepts:Probability & Data Analysis. 3 Credits.
A course for prospective teachers of K-8 mathematics. The course will explore data analysis as a four-step investigative process involving question development, data production, data analysis and contextual conclusions. Topics may include describing and comparing data distributions for both categorical and numerical data, exploring bivariate relationships, exploring elementary probability, and using random sampling as a basis for informal inference. Course includes use of appropriate software. Prerequisite: MATH 222.
MATH 321. Fundamental Concepts:Algebra & Number Theory. 3 Credits.
A course for prospective teachers of K-8 mathematics. Topics chosen from expressions and equations, ratio, proportional relationships and inversely proportional relationships, arithmetic and geometric sequences, factors and multiples (including greatest common factor and least common multiple), prime numbers and the Fundamental Theorem of Arithmetic, divisibility tests, rational versus irrational numbers, the division algorithm, modular arithmetic, functions (linear, quadratic, and exponential). Prerequisite: MATH 222.
MATH 322. Fundamental Concepts:Geometry & Measurement. 3 Credits.
A course for prospective teachers of K-8 mathematics. Perimeter, area, surface area, volume, and angle; geometric shapes, geometric solids, transformations, dilations, symmetry, congruence, similarity; modeling with similar triangles, and the Pythagorean Theorem and its converse. The use of appropriate software is an important component of the course. Prerequisite: MATH 222.
MATH 331. Probability. 3 Credits.
Basic theorems in probability, random variables, distribution functions, expected values; binomial, Poisson and normal distributions. Fall. Prerequisite: Calculus II (MATH 156 or MATH 186 or MATH 188).
MATH 336. Applied Statistics. 3 Credits.
A calculus based survey of probability and statistics with applications in social, natural sciences and engineering. Topics include probability, discrete and continuous random variables, point and interval estimation, hypothesis testing, linear models (encompassing regression and ANOVA). Prerequisite: Calculus II (MATH 156 or MATH 186 or MATH 188).
MATH 361. Introduction to Higher Geometry. 3 Credits.
A survey of axiomatic and modern geometry intended for future middle and high school teachers. Topics covered will include incidence axioms, congruence theorems for triangles, the circle theorems, implications of the fifth postulate, congruence theorems for quadrilaterals, parallelism, similarity, transformational geometry, matrix transformations, and an introduction to spherical and hyperbolic geometry. The course will incorporate the use of Geometers Sketchpad or equivalent software as a tool for verification of conjectures. Offered every other year. Spring. Prerequisite: MATH 243 and MATH 272.
MATH 375. Internship for Juniors. 3 Credits.
MATH 377. Algebra I. 3 Credits.
The first part of a two-semester sequence. An introduction to algebraic structures with an emphasis on groups, covering normal subgroups, cosets. Lagrange's theorem and the fundamental homomorphism theorems. Fall. Prerequisites: MATH 243 and MATH 272.
MATH 385. Vector Calculus. 3 Credits.
Review of vector algebra. Vector-valued functions. Divergence and curl. Multiple integrals; different coordinate systems. Line integrals, Greens Theorem, independence of path, conservative force fields. Surface integrals, Divergence Theorem, Stokes Theorem, Applications. Prerequisites: Calculus III (MATH 285 or MATH 287).
MATH 386. Partial Differential Equations. 3 Credits.
Classification of partial differential equations. Characteristics. Derivation of the classical linear second order equations. Fourier series. Separation of variables. Initial and boundary value problems. Cauchy, Dirichlet, and Neumann problems. Prerequisite: MATH 286.
MATH 387. Analysis I. 3 Credits.
A rigorous treatment of differential calculus of one variable: sequences, limits, continuity, the derivative. Spring. Prerequisites: MATH 243 and Calculus III (MATH 285 or MATH 287).
MATH 422. Seminar for Mathematics Education. 3 Credits.
This course is intended for prospective mathematics teachers. Topics in high school mathematics are examined from an advanced perspective. Topics include the real and complex numbers, functions, equations, and trigonometry. (Enrollment restricted to students in the School of Education and Health.) Spring. Prerequisites: MATH 243 and MATH 272.
MATH 432. Statistical Inference. 3 Credits.
Sampling distributions, point estimation, interval estimation, testing statistical hypotheses, regression and correlation. Spring. Prerequisite: MATH 331.
MATH 433. Advanced Statistics. 3 Credits.
Analysis of variance, regression analysis, non-parametric and sequential tests of hypotheses. Prerequisite: MATH 432.
MATH 448. Combinatorics & Graph Theory. 3 Credits.
Fundamental concepts in combinatorics include binomial coefficients, inclusion-exclusion, and generating functions. Topics in graph theory include connectivity, planarity, colorings and chromatic polynomials, and max-flow-min-cut in networks, and other applications. Not open to students with credit for CMPT 335.
MATH 455. Operations Research. 3 Credits.
Optimization, linear programming, simplex method, duality theory. Transportation problems, scheduling problems, queuing theory. Prerequisite: MATH 272 or permission of instructor.
MATH 457. Machine Learning. 3 Credits.
An introduction to the field of Machine Learning and its real-world applications.
Topics include Supervised & Unsupervised Learning, Bayesian Decision Theory, Nonparametric Methods, Linear Discriminant Functions, Multilayer Neural Networks, Stochastic Methods and Cluster Analysis. Prerequisite: MATH 272 or permission of instructor.
MATH 464. Topology. 3 Credits.
Beginning with a review of set theory and basic topological definitions, topological spaces are studied with metric spaces considered as examples. Compactness, connectedness, metrization theorems. An introduction to homotopy theory. Prerequisite: MATH 243 or permission of instructor.
MATH 471. Linear Algebra II. 3 Credits.
A continuation of the topics introduced in MATH 241( formerly MATH 215) with emphasis on orthogonality, inner product spaces, eigenvalues and eigenvectors, diagonalization, quadratic forms and numerical linear algebra. Fall. Prerequisite: MATH 272.
MATH 475. Internship for Seniors. 3 Credits.
Students participate in an off-campus training experience closely related to their area of mathematics. Frequent meetings with the advisor plus a paper are required. Prerequisites: Senior status, 3.0 GPA, and permission of the student's advisor or the Chair.
MATH 478. Algebra II. 3 Credits.
The second part of a two-semester sequence. Further study of algebraic structures, such as rings, fields and integral domains. The homomorphism theorems and applications. Spring. Prerequisite: MATH 377.
MATH 488. Analysis II. 3 Credits.
A continuation of MATH 387 (or Math 313). Topology of the real numbers, uniform convergence, Riemann integral, infinite series, Taylor and Fourier series, metric spaces. Prerequisite: MATH 387.
MATH 489. Problem Seminar. 3 Credits.
A capstone course for senior mathematics majors. Problems will be chosen to integrate the themes of the major. Oral presentations and mathematical writing and proof will be emphasized. Fall. Prerequisites: MATH 377 and MATH 387 or permission of instructor.
MATH 490. Complex Analysis. 3 Credits.
The complex plane, functions, limits and continuity. Analytic functions, Cauchy- Riemann equations. Cauchy integral theorem and consequences. Additional topics may include: Power series, Taylor and Laurent series, classification of singularities, the Residue Theorem and its applications, conformal mapping, selected applications. Spring. Prerequisite: MATH 286; MATH 243 recommended.
MATH 491. Topics in Mathematics. 3 Credits.
Admission only by permission of the Chair of the Department. This course is offered when demand warrants. Prerequisite: Permission of Chair.
MATH 492. Topics in Mathematics. 3 Credits.
Admission only by permission of the Chair of the Department. This course is offered when demand warrants. Prerequisite: Permission of the chair.
MATH 497. Mathematics Seminar. 3 Credits.
A course limited to students of superior ability who wish to study some advanced topic mutually agreed upon by them, the instructor and the Department Chair. Prerequisite: Permission of the instructor and chair.
MATH 499. Independent Study. 3 Credits.
Individual study or research under faculty supervision. Prerequisite: Permission of the instructor and chair.