Undergraduate Mathematics

"Mathematics is the tool specially suited for dealing with abstract concepts of any kind and there is no limit to its power in this field."
—Paul Dirac (1902–1984)

The Mathematics major at Yeshiva College includes the options of specialized tracks in computer science and actuarial science, and a BA/MA program. Alumni have been accepted to graduate programs at Harvard University, Yale University, Princeton University, Massachusetts Institute of Technology, Brown University, Columbia University, Hebrew University, Courant Institute of Mathematical Sciences at New York University, University of California at Berkeley, Carnegie Mellon University, Rutgers University, the University of California at Los Angeles, and the University of Pennsylvania. Industrial employers of alumni include Google, Citigroup, Travelers Insurance, Merrill Lynch, Deutsche Bank, Northrup Grumman, Deloitte and Touche, Goldman Sachs, Ernst & Young Actuarial Group, and many others. In addition, graduates in the mathematical sciences have served in various advisory capacities, such as the President’s Council of Economic Advisors.

The faculty of the Department of Mathematical Sciences teach at both undergraduate campuses and in The Katz School of Science and Health graduate programs. Topics of faculty research include: partial differential equations, dynamical systems, functional analysis, operator theory, geometric analysis, nonlinear analysis, computational time series analysis, financial mathematics, data science, high-energy physics, plasma dynamics, space-mission design, computational astrophysics, theory of elasticity, mathematical biology, integral equations, and group theory. The research of department faculty has been funded by the National Science Foundation, the National Cancer Institute, the National Aeronautics and Space Administration, the National Institute of Health, and the Department of the Navy. Several of the department faculty have published textbooks in their field.

Stern College for Women has a variety of programs for students interested in the mathematical sciences, which include pure and applied mathematics, industrial mathematics, and scientific programming.

Students interested in industrial applications of mathematics may select the pre-actuarial track, which prepares students for the initial professional examinations for insurance actuaries. The first of these examinations may be used to satisfy the college’s exit requirement. The Career Center will assist in the placement of suitably prepared students in actuarial internships during the summer preceding their senior year.  An undergraduate major in mathematics, supplemented by courses in economics, computer science and business, is also excellent preparation for graduate study in finance or quantitative economics and careers in the financial services industry. Courses in economics, computer science, and physics may be applied to an undergraduate degree in mathematics as correlate courses.

Students who are interested in links between mathematics and computer science may take cross-listed courses in scientific computing, discrete mathematics, and numerical analysis. As many as four computer science courses will be accepted as advanced electives for the mathematics major. A minor in computer science is also offered. Students have the option of pursuing shaped majors that include training in business-related computing and information technology. 

First-year graduate courses in mathematics are open to suitably qualified undergraduates. These currently include courses in risk management and other topics of industrial interest, as well as courses in pure and applied mathematics.

In addition to the Katz graduate program, students may also apply for the BA/MA program, in which they will receive credit toward both the BA and MA degrees for up to 12 credits of graduate courses.

Finally, mathematics is an excellent major for pre-engineering students. Students in the college’s joint engineering programs with Columbia University or the State University of New York at Stony Brook may combine degrees in Computer Science or Computer Engineering at those institutions with a mathematics major at Stern College for Women.

Please see the Schedule of Classes for the current semester’s offerings.

The department of mathematical sciences offers the following degrees: BA in Mathematics (including a pre-actuarial/financial mathematics track), BA/MA in Mathematics (students can receive up to 12 credit hours of graduate courses towards the BA degree, and the remaining graduate courses up to  30 credit hours towards the MA), MA in Mathematics (30 credit hours), and PhD in Mathematics.

Graduate courses in mathematics are open to undergraduate students who successfully completed multivariable calculus and linear algebra.

A mathematics placement examination is required of all students planning to take Math. Students must take this test before registering for MATH 1412.

Mathematics Courses

• STAT 1021 Introduction to Statistics 3 credits
  Sources of data; descriptive statistics: data display, univariate measures of location and variability; basic probability, normal curve and its applications; correlation and regression. Sampling distributions. Inferential procedures in one- and two-sample problems: estimation, hypothesis testing. Chi-square.
• MATH 1010 Excursions in Mathematics 3 credits
  This course is intended for non-science majors and Education majors. Several topics will be taught in depth from the following list: Sets of numbers, geometry, elements of probability and statistics, consumer mathematics, linear programming.
• MATH 1160 Precalculus 4 credits
  Number systems, functions, equations, and inequalities; algebra of polynomials, exponentials, and logarithms; analytic geometry of lines and circles; vectors, trigonometry, and complex numbers. (lecture: 3 hours; recitation: 2 hours).
  Prerequisites: two years of high school mathematics and placement by examination.
• MATH 1410 Fundamentals of Calculus 4 credits
  This course is designed for students majoring in biology, pre-health sciences, or any other major except mathematics, computer science, physics, engineering, chemistry, and physical sciences.  Topics include functions, limits, derivatives, and integrals, and problem solving methods, including optimization and related rates problems. Emphasis is placed on developing and interpreting models from a variety of disciplines, on analyzing data, and on graphing and numerical computations. (lecture: 3 hours; recitation: 1 hour).
  Prerequisite: Pre-Calculus—high school Algebra and Trigonometry.
• MATH 1412, 1413 Calculus I, II 4 credits
  First semester: limits, derivatives, and integrals; continuous and differentiable functions, mean value theorem, chain rule, implicit differentiation. Applications: curve sketching, maxima and minima, related rates, motion, area. Trigonometric, inverse trigonometric, logarithmic and exponential functions. Second semester: methods of integration, area, moments, volume. Indeterminate forms, improper integrals, sequences and series. Parametric equations, arc length and polar coordinates. (lecture: 3 hours; recitation: 2 hours).
  Prerequisites: three years of high school mathematics and placement by examination or MATH 1160.
• MATH 1504 Discrete Structures 4 credits
  Boolean algebra and predicate calculus; proof methods; sets, functions, and relations; combinatorics; graph theory and algorithms; mathematical induction and recursion; probability and average case analysis of algorithms. (lecture: 3 hours; recitation: 2 hours)
  Prerequisite: three years of high school mathematics.
• MATH 1510 Multivariable Calculus 4 credits
  Limits and continuity in Euclidean spaces; partial derivatives, gradient, and chain rule; maxima and minima with constraints; multiple integrals, cylindrical and spherical coordinates; vector calculus; theorems of Green, Gauss, and Stokes.
  Prerequisite: MATH 1413.
• MATH 1520, 1521 Advanced Calculus I, II 3 credits
  Real numbers; theorems on limits; continuous, differentiable, and integrable functions; sequences and series of functions; metric space methods, fixed points, existence theorems for differential equations; implicit function theorem.
  Prerequisites: MATH 1413 and permission of the instructor.
• MATH 1523 Introduction to Analysis 3 credits
  Familiarizes students with analytic tools and ideas that are of practical significance for a variety of applications along with an awareness of the foundations, interrelations, and limitations of those methods.
  Prerequisites: MATH 1510, 2105.
• MATH 1540 Functions of a Complex Variable  3 credits
  Analytic functions, Cauchy Riemann equations, Cauchy integral formula, residue theory, conformal mappings.
  Prerequisite: MATH 1520 or permission of the instructor.
• MATH 2105 Linear Algebra 3 credits
  Systems of linear equations, Gaussian elimination, matrices, matrix algebra; vector spaces, linear transformations, similarity; inner product spaces; determinants; eigenvalues and eigenvectors, diagonalization; quadratic forms; canonical forms; spectral theory; applications.
  Prerequisite: MAT 1412.
• MATH 2168 Elementary Number Theory 3 credits
  Properties of integers, Euclidean algorithm, unique factorization, arithmetic functions, perfect numbers, linear and quadratic congruences, public-key encryption.
• MATH 2215 Modern Algebra 3 credits
  Basic concepts of an algebraic system, a sub-system, a factor-system, an isomorphism and a homomorphism. Examples and initial results from the theory of groups, rings, and fields. The second semester will be devoted to advanced topics, including recent developments.
  Prerequisite: MATH 2105 or permission of the instructor.
• MATH 2461 Probability Theory 3 credits
  Discrete and continuous sample spaces; combinatorial analysis; density and distribution functions of random variables; expectation and variance; independence and conditional probability; law of large numbers; central limit theorem; generating functions; random walk and ruin problems.
  Prerequisite: MATH 1413.
• MATH 2462 Mathematical Statistics 3 credits
  Application of probability theory to the classical parametric models: moment-generating functions, chi-square and t distributions, central limit theorem, sampling distributions, maximum likelihood and interval estimation, confidence intervals, hypothesis testing; nonparametric models; the Bayesian controversy. Examples from natural science and social and behavioral research.
  Prerequisite: MATH 2461.
• MATH 2601 Differential Equations 3 credits
  Classification of differential equations; existence and uniqueness of solutions; initial-value problems, boundary-value problems; power series methods, integral transforms; numerical algorithms and error estimation; topological methods. Prerequisite: MAT 1413.
• MATH 2651 Numerical Analysis 3 credits
  Finite difference calculus; numerical solution of differential equations and linear systems of equations; iterative methods; computation of eigenvalues and eigenvectors. Advanced elective.
  Prerequisite: MATH 1413
• MATH 2901 Mathematics of Finance 3 credits
  Discrete models for options, pricing derivatives, continuous stock price models, Brownian motion, the Black-Scholes formula, the Black-Scholes differential equation, hedging options, dynamic programming, bond price models, yield curves, forwards and futures, Keynes interest rate parity formula.
  Prerequisite: familiarity with differential equations.
• MATH 3301, 3302, 3303, 3304 Topics in Modern Mathematics 3 credits.
  Selected subjects in analysis, algebra, geometry, actuarial, and applied mathematics. Students may register for up to four semesters with permission of the Department Chair.
  Prerequisites: junior status and permission of the instructor.

Mathematics Major

For more details about the Mathematics major and minor - see the factsheet at the Academic Advisement webpage.

• Edward Belbruno
  Clinical Professor of Mathematics (W)
  PhD, New York University
  Research interests:  celestial mechanics, chaos theory, dynamical systems,
  aerospace engineering, cosmology (big bang singularity).
  Contact: edward.belbruno@yu.edu
• 
  Wenxiong Chen
  Professor of Mathematics
  PhD, Academia Sinica
  Research interests: nonlinear elliptic partial differential equations, fractional Laplacians,
  and other non-local operators, nonlinear functional analysis, and geometric analysis.
  Contact: wchen@yu.edu

• Michael Dalezman
  Assistant Professor of Mathematics 
  PhD, New York University
  Research Interests: number theory.
  Contact: dalezma@yu.edu

  Marian Gidea
  Professor of Mathematics, Director of the Graduate Program 
  PhD, SUNY at Buffalo
  Research interests: dynamical systems, chaos theory, celestial mechanics,
  and applications to mathematical physics, astrodynamics, mathematical biology,
  and financial mathematics.
  Contact: marian.gidea@yu.edu

  Steven Gindi
  Postdoctoral Fellow
  PhD, Stony Brook University
  Research interests: differential geometry and mathematical physics - Ricci flow, pluriclosed flow, holomorphic twistor spaces, bihermitian geometry,
  generalized geometry, Poisson geometry.
  Contact: steven.gindi@yu.edu

• Miroslav Iovanov
  Associate Professor of Mathematics
  PhD, SUNY at Buffalo
  Research interests: algebra and related fields, more specifically, including  noncommutative algebra and ring theory, Hopf algebras and quantum groups, representation theory, category theory, combinatorics/discrete math, linear algebra, as well as homological algebra and category theory, topology and combinatorics. 
  Contact: miodrag.iovanov@yu.edu
  
  Antonella Marini, Chair 
  Professor of Mathematics  
  PhD, University of Chicago
  Research interests: partial differential equations and applications to high-energy physics.
  Contact: marini@yu.edu
•  

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Tutoring 

• Tutoring at Yeshiva College is available via Peer Tutoring, Yeshiva College
• Tutoring in mathematics at Stern College for Women is available via Tutoring - Math/Calculus

Research

• Interactive Models of the Hyperbolic Plane
• Software created by a faculty member at the University of New Mexico.
• Kolmogorov
  Links and resources related to the work of the great Soviet mathematician.
• Grothendieck
  Links and resources related to the work of the great algebraic geometer.

Internships

• Mathematics Internships
  A listing maintained by a professor at Purdue University.
• Internships, Scholarships, and Awards
  From the American Statistical Association.
• Internships and Co-op Opportunities
  From the American Mathematical Society.
• NASA Internships

Graduate Study

• Graduate Fellowships in Mathematics (PDF)
  From the American Mathematical Society.
• Graduate Fellowships in Applied Mathematics
  From the Society for Industrial and Applied Mathematics.

Careers

• Careers in Mathematics
  From the American Mathematical Society.
• Careers in Applied Mathematics
  From the Society for Applied Mathematics.
• Actuarial Careers
  From Be An Actuary.
• Careers in Risk Management
  From the Society of Actuaries.
• Careers in Statistical Analysis
  From the American Statistical Association

News and Organizations

• The Isaac Newton Institute for Mathematical Sciences
  In Cambridge, England
• The Santa Fe Institute
• The Center for Nonlinear Studies
• The American Institute of Mathematics
• American Mathematical Society
• American Statistical Association
• Society for Applied Mathematics