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Mathematics

 

Dr. Helene R. Tyler
Chair of the Department

Dr. Matthew Jura
Assistant 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 through 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, and teaching, as well as to prepare for the study of mathematics at the graduate level.  Coursework in linear algebra, abstract algebra, analysis, probability, and statistics prepare students for further work in pure or applied mathematics.  Elective courses, such as Operations Research, Machine Learning, and Mathematical Modeling, provide students the tools to analyze data in various areas of science, finance, and engineering.

Our classes are small, giving students the opportunity to build strong relationships with faculty.  Students are invited to participate in national mathematics competitions such as the Putnam Exam.  Many students participate in undergraduate research projects, both internal and external; funds are available to support these projects during the summer.  Students are encouraged to present their work at national and regional meetings, including the Spuyten Duyvil Undergraduate Mathematics Conference, which was founded by the Mathematics Department at Manhattan College.

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. 

Students in the Department of Mathematics are eligible to participate in the School of Science Honors Program.  See the School of Science catalog entry for more information on this program.

The Department supports a chapter 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

The Department also offers graduate programs in Mathematics.  We have a seamless 5-year Bachelor-Masters  program.  A student in this 5-year B.A./B.S.-M.S. program graduates with a B.A./B.S. in Mathematics and an M.S. in Applied Mathematics-Data Analytics.  In addition, the Department offers an M.S. in Mathematics.  See the Graduate Catalog for more details.

The Department works closely with the School of Education & Health on the requirements for the B.S. in Adolescence Education Mathematics, which prepares students to teach at the secondary level, and the Mathematics emphasis in the B.S. in Childhood Education, which prepares students to teach at the elementary level. The requirements for the B.S. 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.  These plans incorporate the School of Science Core Curriculum.  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).

With the approval of the Department Chair, well-prepared undergraduate students can take graduate mathematics courses to count toward their mathematics electives.

Major in Mathematics

B.S. in Mathematics     (126 credit hours)

MATH 158Introduction to Mathematical Computation3
MATH 185Calculus I *3
MATH 186Calculus II *3
MATH 243Foundations for Higher Mathematics3
MATH 285Calculus III *3
MATH 331Probability3
MATH 336Applied Statistics3
MATH 372Linear Algebra I3
MATH 377Algebra I3
MATH 387Analysis I3
MATH 471Linear Algebra II3
MATH 478Algebra II3
MATH 489Problem Seminar3
MATH 490Complex Analysis3
MATH Electives **6
CMPT 101Computer Science I3
PHYS 101
PHYS 191
Physics I
and Physics I Lab
4
PHYS 102
PHYS 192
Physics II
and Physics II Lab
4
Natural Sciences8
Total Credits67

B.A. in Mathematics     (122 credit hours)

MATH 158Introduction to Mathematical Computation3
MATH 185Calculus I *3
MATH 186Calculus II *3
MATH 243Foundations for Higher Mathematics3
MATH 285Calculus III *3
MATH 331Probability3
MATH 336Applied Statistics3
MATH 372Linear Algebra I3
MATH 377Algebra I3
MATH 387Analysis I3
MATH 471Linear Algebra II3
MATH 478Algebra II3
MATH 489Problem Seminar3
MATH 490Complex Analysis3
MATH Electives **6
CMPT 101Computer Science I3
3 SCI Courses ***9
Total Credits60

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 (excluding MATH 158).  These credits must include MATH 185 (or 187), 186 (or 188), 243, 285 (or 287), 336, 372, 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.

B.S. in Adolescence Education Mathematics

MATH 158Introduction to Mathematical Computation3
MATH 185Calculus I3
MATH 186Calculus II3
MATH 243Foundations for Higher Mathematics3
MATH 285Calculus III3
MATH 328Fundamental Concepts of Secondary Mathematics3
MATH 331Probability3
MATH 336Applied Statistics3
MATH 361Introduction to Higher Geometry3
MATH 372Linear Algebra I3
MATH 377Algebra I3
MATH 387Analysis I3
MATH 489Problem Seminar3
CMPT 101Computer Science I3
Total Credits42

Application:  To pursue a Second Major in Mathematics, a student must get the appropriate form from the department, fill it out, and have it approved by the Department of Mathematics.  An approved form will be forwarded to the appropriate dean. 

A grade of at least C is required for all courses meeting the requirements for a Second Major in Mathematics.

Concentration in Applied Mathematics

The 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 requires 24 credits and offers more depth than the minor in Mathematics.  A grade of at least C is required for all courses meeting the requirements for a Concentration in Applied Mathematics.

The requirements are flexible. There is a required core of 12 credits which includes Calculus I-II-III (MATH 185/187, 186/188, 285/287) and Linear Algebra I (MATH 372). Students choose the remaining 12 credits from a list of approved courses, including Differential Equations (MATH 286), Probability (MATH 331), Applied Statistics (MATH 336), Partial Differential Equations (MATH 386), Machine Learning (MATH 457), Operations Research (MATH 455), Linear Algebra II (MATH 471), and Topics in Mathematics.  Graduate mathematics courses can also be used with approval of the Chair. 

Students must select at least one two-term sequence for depth.  The two-term sequences are:  372 and 471; (285 or 287) and 490; 286 and 386; 331 and 336. 

Completion of the Concentration will be documented on the student's transcript. 

Application:  To pursue the Concentration in Applied Mathematics, a student must get the appropriate form from the department, fill it out, and have it approved by the Department of Mathematics.  An approved form will be forwarded to the appropriate dean. 

Minor in Mathematics 

The minor in Mathematics consists of a minimum of 15 credits and must include a yearlong calculus sequence.  Specific requirements are listed below.  A grade of at least 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, 154, 158, 221, 222, 230, 320, 321, 322, 326, 328, 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 approved by the Department of Mathematics.  An approved form will be forwarded to the appropriate dean. 

Minor Requirements
The minor in Mathematics consists of a minimum of 15 credits including Calculus I (MATH 155/185/187) and Calculus II (MATH 156/186/188).  The remaining courses should be chosen from mathematics courses that are not on the above list of courses which may not be used toward the Mathematics minor, with the approval of the Chair of the Department of Mathematics.  

B.S. in Childhood Education - Mathematics Plans

All students majoring in Childhood Education take the following 6 credit core sequence. 

MATH 221Mathematics for the Elementary School Teachers I3
MATH 222Mathematics for the Elementary School Teachers II3

In addition, students majoring in Childhood Education may choose to do either a Concentration in Mathematics or an Emphasis in Mathematics as detailed below.

B.S. in Childhood Education – Mathematics Concentration
Childhood Education majors may choose to concentrate in Mathematics.  These students take 30 credits in Mathematics including Calculus I (MATH 155/185/187), Calculus II (MATH 156/186/188), MATH 243, 321, 322, 326, One of 230 or 336, Three from the following: 372, 285, 286, 331, 361.  Please see the Department of Mathematics for the appropriate sequencing of these courses.

B.S. in Childhood Education – General Studies Concentration with Mathematics Emphasis
Childhood Education majors may choose a General Studies Concentration with Mathematics as one area of emphasis.  These students take 15 credits in Mathematics including MATH 321, 322, 326, 230, One of: 100, 151, 155, 185.  Please see the Department of Mathematics for the appropriate sequencing of these courses.

PLANS OF STUDY

Bachelor of Science in Mathematics

First Year
FallCreditsSpringCredits
MATH 1853MATH 158**3
CMPT 1013MATH 1863
MFL*3MFL*3
ENGL 1103RELS 1103
LLRN 1023Social Science3
SCI 1001SCI 1011
 16 16
Second Year
FallCreditsSpringCredits
MATH 2433MATH 3363
MATH 2853MATH 3723
PHYS 101
PHYS 191
4PHYS 102
PHYS 192
4
PHIL 1503ENGL 1503
Social Science3Free Elective3
 16 16
Third Year
FallCreditsSpringCredits
MATH 3313MATH 3873
MATH 3773MATH 4783
MATH 4713RELS 2XX Catholic Studies3
Natural Science***4Natural Science***4
HIST 1503MUSC 150 or ART 1503
 16 16
Fourth Year
FallCreditsSpringCredits
MATH 4903MATH 4893
MATH Elective3MATH Elective3
Free Electives9Free Electives6
 RELS 3XX Global/Contemporary3
 15 15
Total Credits: 126

Bachelor of Arts in Mathematics

First Year
FallCreditsSpringCredits
MATH 1853MATH 158**3
CMPT 1013MATH 1863
MFL*3MFL*3
ENGL 1103RELS 1103
LLRN 1023Social Science3
SCI 1001SCI 1011
 16 16
Second Year
FallCreditsSpringCredits
MATH 2433MATH 3363
MATH 2853MATH 3723
SCI XXX***3SCI XXX***3
PHIL 1503SCI XXX***3
Social Science3ENGL 1503
 15 15
Third Year
FallCreditsSpringCredits
MATH 3313MATH 3873
MATH 3773MATH 4783
MATH 4713RELS 2XX Catholic Studies3
HIST 1503MUSC 150 or ART 1503
Free Elective3Free Elective3
 15 15
Fourth Year
FallCreditsSpringCredits
MATH 4903MATH 4893
MATH Elective3MATH Elective3
Free Electives9RELS 3XX Global/Contemporary3
 Free Electives6
 15 15
Total Credits: 122

Bachelor of Science Adolescence Education Mathematics 

Sequencing of Mathematics Courses

See the Department of Education for sequencing of Education Courses.

First Year
FallCreditsSpringCredits
MATH 1853MATH 158*3
CMPT 1013MATH 1863
 6 6
Second Year
FallCreditsSpringCredits
MATH 2433MATH 3283
MATH 2853MATH 3723
 6 6
Third Year
FallCreditsSpringCredits
MATH 3313MATH 3873
MATH 3773MATH 3613
 6 6
Fourth Year
 SpringCredits
 MATH 3363
 MATH 4893
 6
Total Credits: 42

Courses

MATH 096. Bridge Course for Business. 0 Credits.

A review of the fundamentals of algebra, functions and their graphs, logarithmic and exponential functions, Excel spreadsheets. Intended for incoming business students with marginal non-passing TRAM scores. The student must obtain a passing grade to be placed into MATH 153.

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 incoming students in science and engineering with marginal non-passing TRAM scores. The student must obtain a passing grade to be placed into MATH 185 Calculus I.

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 Mathematics. 3 Credits.

An introduction to practical mathematical topics of particular interest to students in the humanities or social sciences. Possibilities include but are not limited to the mathematics of social choice, consumer mathematics, mathematical modeling and statistics. Additional topics may be introduced as time permits.

MATH 153. Finite Mathematics for Business Decisions. 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 a grade of 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, exponential and logarithmic functions. Limits, derivatives, techniques and applications of differentiation. Indefinite and definite integrals, applications of the integral. Prerequisite: A passing grade in MATH 153.

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 grade of 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: A grade of C or better in 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. A variety of problems arising in mathematics, science, and engineering. Spring. Prerequisite: A grade of C or better in CMPT 101 and Calculus I (MATH 155 or MATH 185 or MATH 187).

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 grade of 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.

Honors equivalent to Calculus I. Rigorous development of 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. Fall. Prerequisite: Students will be selected by the instructor.

MATH 188. Honors Calculus II. 3 Credits.

Honors equivalent to Calculus II. Rigorous development of applications of the definite integral, integration techniques, improper integrals, and infinite sequences and series. Meets four hours per week. Spring. Prerequisite: A grade of C or better in MATH 187 or permission of the instructor.

MATH 221. Mathematics for the Elementary School Teachers I. 3 Credits.

This is a course for prospective teachers in elementary school. 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. Fall.

MATH 222. Mathematics for the Elementary School Teachers II. 3 Credits.

This is a course for prospective teachers in elementary school. 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. Spring. Prerequisite: A grade of C or better in 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. Foundations for Higher Mathematics. 3 Credits.

A bridge between introductory and advanced mathematics. The context of set theory and logic will be used to develop the skills of constructing and interpreting mathematical proofs. Topics include principles of logical argument, modular arithmetic, induction, sets, relations, functions, equivalence relations. Fall. Prerequisites: A grade of C or better in Calculus II (MATH 156 or MATH 186 or MATH 188) or current enrollment in Calculus II (MATH 156 or MATH 186 or MATH 188).

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 156, 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 linear differential equations. Methods include separation of variables, variation of parameters, and the Laplace transform. Prerequisite: A grade of C or better in 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). Fall. Prerequisite: A grade of C or better in 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: A grade of C or better in 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: A grade of C or better in 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: A grade of C or better in MATH 222.

MATH 326. Fundamental Concepts: Discrete Math. 3 Credits.

A course for prospective teachers of K-8 mathematics. Topics chosen from logic, Boolean algebra, introductory graph theory, counting techniques and mathematical induction. Coding will be introduced as a way of including technology as well as algorithmic, iterative and recursive thinking into the course. Prerequisite: A grade of C or better in MATH 222.

MATH 328. Fundamental Concepts of Secondary Mathematics. 3 Credits.

A course for prospective teachers of secondary school mathematics. There will be a strong emphasis on the high school Common Core Standards and Mathematical Practices. Central ideas from the following topics will be explored and connected from both intuitive and rigorous points of view. Topics include the real and complex numbers, transcendental functions, exponentiation, hyperbolas, ellipses, logarithmic functions, polynomials, statistics, probability, and trigonometry. Appropriate technological tools will be used. Prerequisites: A grade of C or better in MATH 243.

MATH 331. Probability. 3 Credits.

Basic theorems in probability, random variables, distribution functions, expected values; binomial, Poisson and normal distributions. Fall. Prerequisite: A grade of C or better in 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 and natural sciences and engineering. Topics include probability, discrete and continuous random variables, point and interval estimation, hypothesis testing, linear models (encompassing regression and ANOVA). Not open to students with credit for MATH 351. Spring. Prerequisite: A grade of C or better in Calculus II (MATH 156 or MATH 186 or MATH 188).

MATH 351. Computational Linear Algebra & Statistics for Computer Science. 3 Credits.

This course consists of three components: linear algebra including linear equations and matrices, vector spaces, subspaces, linear independence, bases, dimension, linear transformations, eigenvalues/eigenvectors, and diagonalization; Operations research including linear programming and the simplex method; Statistical inference including point and interval estimation, bias, hypothesis testing, linear models (encompassing regression and ANOVA). Enrollment restricted to Computer Science students or by approval of Department Chair. Not open to students with credit in (MATH 272 or MATH 372 or MATH 336).A grade of C or better in 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 appropriate software as a tool for verification of conjectures. Spring. Prerequisite: A grade of C or better in MATH 243 and Co-requisites: MATH 272 or MATH 372 or MATH 351.

MATH 372. 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. Not open to students with credit for MATH 351. Prerequisite: A grade of C or better in MATH 243 or MATH 285 or MATH 287.

MATH 375. Internship for Juniors. 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: Junior status, 3.0 GPA and permission of the student's advisor or Department chair.

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: A grade of C or better in MATH 243 and (MATH 272 or MATH 372 or MATH 351).

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. Offered irregularly. Prerequisites: A grade of C or better in 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: A grade of C or better in MATH 286.

MATH 387. Analysis I. 3 Credits.

A rigorous treatment of differential calculus of one variable: sequences, limits, continuity, the derivative, the Riemann integral. Spring.Prerequisites: A grade of C or better in MATH 243 and Calculus III (MATH 285 or MATH 287).

MATH 422. Seminar for Mathematics Education. 3 Credits.

This course is intended for prospective secondary mathematics teachers. Topics in high school mathematics are examined from an advanced perspective. Topics include the real and complex numbers, functions, equations, and trigonometry. Spring. Prerequisites: A grade of C or better in MATH 243 and (MATH 272 or MATH 372 or MATH 351).

MATH 432. Statistical Inference. 3 Credits.

Sampling distributions, point estimation, interval estimation, testing statistical hypotheses, regression and correlation. Offered irregularly. Prerequisite: A grade of C or better in MATH 331.

MATH 433. Advanced Statistics. 3 Credits.

Analysis of variance, regression analysis, non-parametric and sequential tests of hypotheses. Offered irregularly. Prerequisite: A grade of C or better in MATH 432.

MATH 448. Combinatorics & Graph Theory. 3 Credits.

Fundamental concepts in combinatorics including 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. Prerequisite: A grade of C or better in MATH 243.

MATH 455. Operations Research. 3 Credits.

Optimization, linear programming, simplex method, duality theory. Transportation problems, scheduling problems, queuing theory. Prerequisite: A grade of C or better in MATH 272 or MATH 372 or MATH 351 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: A grade of C or better in MATH 272 or MATH 372 or MATH 351 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: A grade of C or better in MATH 243 or permission of instructor.

MATH 471. Linear Algebra II. 3 Credits.

A continuation of the topics introduced in MATH 372 with emphasis on orthogonality, inner product spaces, eigenvalues and eigenvectors, diagonalization, quadratic forms and numerical linear algebra. Fall. Prerequisite: A grade of C or better in MATH 372.

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 Department Chair.

MATH 478. Algebra II. 3 Credits.

A continuation of MATH 377. Further study of algebraic structures, such as rings, fields and integral domains. The homomorphism theorems and applications. Spring. Prerequisite: A grade of C or better in MATH 377.

MATH 488. Analysis II. 3 Credits.

A continuation of MATH 387. Topology of the real numbers, uniform convergence, Riemann integral, infinite series, Taylor and Fourier series, metric spaces. Prerequisite: A grade of C or better in 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: A grade of C or better in 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: A grade of C or better in (MATH 243 and MATH 285) or MATH 286 or permission of instructor.

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 the Department 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 Department 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 the Department Chair.

MATH 499. Independent Study. 1-3 Credit.

Individual study or research under faculty supervision. Prerequisite: Permission of the instructor and the Department Chair.