Mathematics
Dr. Carol M. Hurwitz
Chair of the Department
The mathematics curriculum introduces students to technology, encourages student research and features yearlong sequences in Linear and Abstract Algebra, as well as a wealth of upper division electives, including pure and applied mathematics and computer science. Classes are small, giving students the opportunity to build strong relationships with faculty. Students are invited to participate in national competitions such as the Putnam Exam and the Mathematical Modeling Contest. Many of our students present projects at the Spuyten Duyvil Undergraduate Mathematics Conference, which was founded by the Manhattan College Mathematics and Computer Science Department. Funds are available to support undergraduate research projects during the summer and students have also attended summer undergraduate research programs.
General Requirements: Major courses should be taken in accordance with the PLAN OF STUDY listed below. The order in which core courses are taken is flexible. A minimum grade of C in each of the major courses is required. Before taking any major course, the student must obtain a grade of C or better in the prerequisite courses.
Major in Mathematics
A major program in mathematics is available in the School of Science leading to either a Bachelor of Science or a Bachelor of Arts degree. The requirements for these degrees are shown below.
BS in Mathematics
| MATH 185 | Calculus I * | 3 |
| MATH 186 | Calculus II * | 3 |
| MATH 243 | Foundations for Higher Mathematics | 3 |
| MATH 272 | Linear Algebra I | 3 |
| MATH 285 | Calculus III * | 3 |
| MATH 286 | Differential Equations | 3 |
| MATH 331 | Probability | 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 |
| CMPT 102 | Computer Science II | 3 |
| PHYS 101 | Physics I | 4 |
| PHYS 102 | Physics II | 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 MATH 185 and MATH 186. MATH 287 replaces MATH 285. |
BA in Mathematics
| MATH 185 | Calculus I * | 3 |
| MATH 186 | Calculus II * | 3 |
| MATH 243 | Foundations for Higher Mathematics | 3 |
| MATH 272 | Linear Algebra I | 3 |
| MATH 285 | Calculus III * | 3 |
| MATH 286 | Differential Equations | 3 |
| MATH 331 | Probability | 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 |
| CMPT 102 | Computer Science II | 3 |
| 3 SCI xxx 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 MATH 185 Calculus I and MATH 186 Calculus II. MATH 287 Honors Calculus III replaces MATH 285 Calculus III. |
Minor in Mathematics
A minimum of 15 credits, or five approved courses, including MATH 185 (formerly MATH 103) Calculus I, MATH 186 (formerly MATH 104) Calculus II, MATH 285 (formerly Math 201) Calculus III or MATH 287((formerly Math 209) Honors Calculus III. A minimum grade of C is required in all courses. A student may use at most one course transferred from another institution toward the Minor. Four courses must be taken in the Department of Mathematics at Manhattan College.
Note: MATH 100, MATH 151, MATH 153, MATH 221, MATH 222, MATH 230, MATH 321, and MATH 422 may not be used toward the Math minor. MATH 361 is not suitable for engineering students. In the old numbering system, these courses correspond to MATH 100, MATH 102, MATH 105, MATH 211, MATH 221, MATH 222, MATH 307, and MATH 466.
Application: When the required courses are completed, a student must get a Minor Form from the department secretary, fill it out and have it signed by the Chair of the Department.
Requirements for Students in the School of Education
Adolescence Education
| Mathematics Requirements * | ||
| MATH 185 | Calculus I | 3 |
| MATH 186 | Calculus II | 3 |
| MATH 243 | Foundations for Higher Mathematics | 3 |
| MATH 272 | Linear Algebra I | 3 |
| MATH 285 | Calculus III | 3 |
| MATH 361 | Introduction to Higher Geometry | 3 |
| MATH 331 | Probability | 3 |
| MATH 377 | Algebra I | 3 |
| MATH 387 | Analysis I | 3 |
| MATH 432 | Statistical Inference | 3 |
| MATH 489 | Problem Seminar | 3 |
| MATH 422 | Seminar for Mathematics Education | 3 |
| Computer Science Requirements | ||
| CMPT 101 | Computer Science I | 3 |
| CMPT 102 | Computer Science II | 3 |
| CMPT 214 | Teaching and Learning with Technology | 3 |
| * | Sequencing of courses is very important, so that only one course is required during the semester when the student is doing student teaching. MATH 331 Probability (Fall) and MATH 432 Statistical Inference (Spring) are a one-year sequence and should be taken in the junior year. |
Childhood Education
| MATH 221 | Mathematics for Elementary School Teachers I | 3 |
| MATH 222 | Mathematics for Elementary School Teachers II | 3 |
PLAN OF STUDY
Bachelor of Science in Mathematics
| First Year | |||
|---|---|---|---|
| Fall | Credits | Spring | Credits |
| MATH 185 | 3 | MATH 186 | 3 |
| CMPT 101 | 3 | CMPT 102 | 3 |
| MLL* | 3 | MLL* | 3 |
| ENGL 110 | 3 | RELS 110 | 3 |
| LLRN 102 | 3 | Social Science | 3 |
| 15 | 15 | ||
| Second Year | |||
| Fall | Credits | Spring | Credits |
| MATH 285 or 287 | 3 | MATH 286 | 3 |
| MATH 243 | 3 | MATH 272 | 3 |
| PHYS 101 | 4 | PHYS 102 | 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 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 Global/Contemporary | 3 | ||
| 15 | 15 | ||
| Total Credits: 124 | |||
| * | One year sequence of a modern foreign language. |
| ** | One year (8 credits with lab) of the same natural science is required. |
Bachelor of Arts in Mathematics
| First Year | |||
|---|---|---|---|
| Fall | Credits | Spring | Credits |
| MATH 185 | 3 | MATH 186 | 3 |
| CMPT 101 | 3 | CMPT 102 | 3 |
| MLL* | 3 | MLL* | 3 |
| ENGL 110 | 3 | RELS 110 | 3 |
| LLRN 102 | 3 | Social Science | 3 |
| 15 | 15 | ||
| Second Year | |||
| Fall | Credits | Spring | Credits |
| MATH 285 or 287 | 3 | MATH 286 | 3 |
| MATH 243 | 3 | MATH 272 | 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 Catholic Studies | 3 |
| HIST 150 | 3 | MUSC 150 or ART 150 | 3 |
| Free Electives | 3 | Free Electives | 3 |
| 15 | 15 | ||
| Fourth Year | |||
| Fall | Credits | Spring | Credits |
| MATH 489 | 3 | MATH 490 | 3 |
| MATH Elective | 3 | RELS Global/Contemporary | 3 |
| Social Sciences | 3 | MATH Elective | 3 |
| Free Electives | 6 | Free Electives | 6 |
| 15 | 15 | ||
| Total Credits: 120 | |||
| * | One year sequence of a Modern Foreign Language. |
| ** | Students may opt for one (1) full year of a lab science (8 credits). In this case, an additional course must be taken to achieve a total of 120 credits. |
| *** | If MATH 432 Statistical Inference is chosen as a Math Elective, it should be taken right after MATH 331 Probability. |
Courses
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 109. Honors Calculus I. 3 Credits.
Rigorous development of differential and integral calculus. Restricted to select students who will take these courses in lieu of MATH 185, MATH 186. (Meets four hours per week).
MATH 110. Honors Calculus II. 3 Credits.
Rigorous development of differential and integral calculus. Restricted to select students who will take these courses in lieu of MATH 185, MATH 186. (Meets four hours per week).
MATH 111. Pre-Calculus Mathematics. 3 Credits.
(For students in the School of Business only.) 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. Modern Mathematics. 3 Credits.
(Formerly MATH 102) The mathematics of voting. Mathematics of fair division. Mathematics of apportionment. Graph theory. Consumer mathematics. Probability.
MATH 153. Linear Math Analysis. 3 Credits.
(Formerly Math 105) 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.
MATH 154. Calculus Business Decisions. 3 Credits.
(Formerly Math 106) 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: MATH 105 or MATH 153.
MATH 155. Calculus for the Life Sciences I. 3 Credits.
(Formerly MATH 121) 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 is necessary to enroll in MATH 155.
MATH 156. Calculus for the Life Sciences II. 3 Credits.
(Formerly MATH 122) 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. Pre-requisite: MATH 121 or MATH 155.
MATH 185. Calculus I. 3 Credits.
(Formerly Math 103) Limits, derivatives, continuity, differentiation and an introduction to the definite integral, and area between curves.(Meets four hours per week). Students are reminded that a grade of C- or lower in MATH 185 (formerly MATH 103) may indicate inadequate preparation for MATH 186 (formerly MATH 104). Prerequisite: A satisfactory score on the mathematics placement exam is necessary to enroll in MATH 185.
MATH 186. Calculus II. 3 Credits.
(Formerly Math 104) Applications of the definite integral, transcendental functions, integration techniques and infinite series. (Meets four hours per week). Students are reminded that a grade of C- or lower in MATH 185 (formerly MATH 103) may indicate inadequate preparation for MATH 186. Prerequisite: MATH 103 or MATH 185.
MATH 221. Mathematics for 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, and number theory.
MATH 222. Mathematics for 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, and trigonometry.
MATH 230. Elementary Statistics. 3 Credits.
(Formerly MATH 211) 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 242. Discrete Mathematics for Computer Science. 3 Credits.
(Formerly MATH 216) An introduction to the mathematical concepts and techniques most frequently needed in the study of computer science: logic, induction, sets and relations, matrix algebra, and recursion. Prerequisite: MATH 104 or MATH 186 or permission of the chair.
MATH 243. Foundations for Higher Mathematics. 3 Credits.
(Formerly MATH 213) This course will serve as 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, congruence modulo, induction, sets, functions, relations, equivalence relations, countability and uncountability of sets. Prerequisite: MATH 104 or MATH 186 or permission of instructor.
MATH 272. Linear Algebra I. 3 Credits.
(Formerly MATH 215)Linear equations and matrices, vector spaces, sub spaces, linear independence, bases, dimension, inner product spaces, linear transformations, eigenvalues and eigenvectors, orthogonal matrices and diagonalization. Prerequisite: MATH 213 or MATH 243 or permission of instructor.
MATH 285. Calculus III. 3 Credits.
(Formerly Math 201)
Algebraic and geometric aspects of vectors, functions of several variables, partial derivatives and multiple integrals. Prerequisite: MATH 104 or MATH 122 or MATH 186 or MATH 156.
MATH 286. Differential Equations. 3 Credits.
(Formerly MATH 203) This course focuses on techniques of solving first and second order ordinary differential equations. Methods include separation of variables, variation of parameters, and the Laplace transform. Applications include linear and nonlinear models. Prerequisite: MATH 201 or MATH 209 or MATH 285 or MATH 287 or permission of the instructor.
MATH 287. Honors Calculus III. 3 Credits.
(Formerly 209) Honors equivalent to Calculus III. Algebraic and geometric aspects of vectors, functions of several variables, partial derivatives and multiple integrals. Intended to be for students who have completed the honors section of MATH 104 or MATH 186. Prerequisite: Honors section of MATH 104 or MATH 186 or permission of the instructor.
MATH 321. Fundammental Concepts. 3 Credits.
(Formerly Math 307) A course for prospective teachers of mathematics. There will be a strong concentration on the Topics of the New York State Regents Syllabus for secondary school mathematics. There will also be a computer component of the course which will include some work with current educational software. Mathematical topics will include sets, proofs, symbolic logic, analytic geometry and basic probability and statistics. Prerequisites: MATH 103, MATH 104 or MATH 185, MATH 186.
MATH 331. Probability. 3 Credits.
(Formerly MATH 420) Basic theorems in probability, random variables, distribution functions, expected values; binomial, Poisson and normal distributions. Fall.
Prerequisite: MATH 104 or MATH 186.
MATH 336. Applied Statistics. 3 Credits.
(Formerly Math 333) 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: MATH 104 or MATH 186.
MATH 361. Introduction to Higher Geometry. 3 Credits.
(Formerly MATH 311) 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. Prerequisites: MATH 213, MATH 215 or MATH 243, MATH 272.
MATH 375. Internship for Juniors. 3 Credits.
Students participate in an off-campus training experience closely related to one of the areas 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 the Chair.
MATH 377. Algebra I. 3 Credits.
(Formerly Math 315) 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 213, MATH 215 or MATH 243, MATH 272.
MATH 385. Vector Calculus. 3 Credits.
(Formerly Math 305)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. Prerequisite: MATH 201 or MATH 209 or MATH 285 or MATH 287.
MATH 386. Partial Differential Equations. 3 Credits.
(Formerly MATH 308) 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 203 or MATH 286.
MATH 387. Analysis I. 3 Credits.
(Formerly Math 313) A rigorous treatment of differential calculus of one variable: sequences, limits, continuity, the derivative. Fall. Prerequisites: MATH 201 and MATH 213 or MATH 285 and MATH 243.
MATH 422. Seminar for Mathematics Education. 3 Credits.
(Formerly Math 466) 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 213, MATH 215 or 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 420 or MATH 331.
MATH 433. Advanced Mathematical Statistics I. 3 Credits.
(Formerly MATH 423) Analysis of variance, regression analysis, non-parametric and sequential tests of hypotheses. Prerequisite: MATH 421 or MATH 432.
MATH 455. Operations Research. 3 Credits.
(Formerly MATH 425) Optimization, linear programming, simplex method, duality theory. Transportation problems, scheduling problems, queuing theory.
Prerequisite: MATH 215 or MATH 272 or permission of instructor.
MATH 457. Topics in Applied Mathematics. 3 Credits.
(Formerly MATH 465) Topics covered include Fourier series, partial differential equations, the Laplace Transform.
MATH 464. Topology. 3 Credits.
(Formerly Math 417) 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 213 or MATH 243 or permission of instructor.
MATH 471. Linear Algebra II. 3 Credits.
(Formerly Math 325) 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 215 or 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.
(Formerly Math 316)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 315 or MATH 377.
MATH 488. Analysis II. 3 Credits.
(Formerly Math 314) 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 203 and MATH 213 or MATH 286 or MATH 243.
MATH 489. Problem Seminar. 3 Credits.
(Formerly Math 460) 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. Spring. Prerequisites: MATH 313 or MATH 315 or MATH 387, MATH 377 or permission of instructor.
MATH 490. Complex Analysis. 3 Credits.
(Formerly MATH 407) 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 203, MATH 213 recommended or MATH 286, MATH 243 recommended or permission of instructor.
MATH 491. Topics in Mathematics. 3 Credits.
(Formerly MATH 461-462) Admission only by permission of the Chair of the Department. This course is offered when demand warrants. Prerequisite: Permission of the chair.
MATH 492. Topics in Mathematics. 3 Credits.
(Formerly Math 461-462) 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.
(Formerly MATH 467) 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.
(Formerly Math 469) Individual study or research under faculty supervision. Prerequisite: Permission of the instructor and chair.