Mathematics BS (Florham)
Math majors develop many skills including the ability to formulate and solve problems, logical and critical thinking, numerical computation, and quantitative skills. These skills are crucial in many fields. Career opportunities include working as a Mathematician, Computer Scientist, Statistician, Economist, Actuary, Cryptologist, Biostatistician, and College Professor.
NOTE: All students are required to complete the General Education Requirements of their campus in fulfillment of their Bachelor degree requirements.
6 credits from the MAJOR may be applied toward General Education Requirements.
Required Mathematics (24 credits)
- MATH1203 Calculus I
- MATH2202 Calculus II
- MATH2203 Calculus III
- MATH3318 Differential equations
- MATH2255 Discrete Structures
- MATH3220 Linear Algebra
- MATH3225 Abstract Algebra
- MATH3231 Introductory Analysis
- MATH3232 Multivariable Advanced Calculus
- MATH3303 Probability and Statistics
- MATH4999 Mathematics Assessment
Major Elective Courses (15 – 18 credits)
At least five courses to be selected from the mathematics offerings (MATH designation) above the level of MATH2255, or with the permission of the department, from the graduate offerings in mathematics; up to 6 credits from the 2000 (or higher level) offerings in computer science (CSCI designation) may be substituted for mathematics electives.
NOTE: At least one of the following pairs of courses must be completed:
- Pair I: MATH3231 Introductory Analysis; MATH3335 Complex Variables
- Pair II: MATH3318 Differential Equations; MATH3309 Numerical Analysis
- Pair II: MATH3210 Number Theory; MATH3225 Abstract Algebra
- Pair IV: MATH3371 Modeling and Simulation; MATH3318 Differential Equations
- Pair V: MATH2255 Discrete Structures; MATH3306 Combinatorics
- Pair VI: MATH3220 Linear Algebra; MATH3331 Higher Geometry
- Pair VII: MATH3303 Probability and Statistics; MATH3305 Advanced Probability and Statistics
NOTE: Three credits in Internship experience may be used to fulfill Major Elective requirements in additional to the 15 credits minimum requirement.
To fulfill the general education requirements, they are required to take:
PHYS2003, PHYS2013 and PHYS2004, PHYS2014 General Physics with Calculus I and II.
Cognate requirements (3 credits)
- CSCI2215 Introduction to Computer Science
6 credits from the MINOR may be applied toward General Education Requirements.
CSCI2215 Introduction to computer hardware and software, their interaction and trade-offs. Essentials of a computer organization and arithmetic, programming languages, assemblers, compilers and interpreters, I/O devices, operating systems, databases and files. Basic ideas in the areas of computer networks, system organization, computer theory, and security. Foundation for more advanced courses.
MATH1203 Slope of a straight lines, slopes of a curve, rate of change of functions, derivatives of algebraic and trigonometric functions, maxima and minima, Mean Value Theorem, indefinite and definite integrals and their applications.
MATH2202 Differentiation and integration of transcendental functions, methods of integration, indeterminate forms, infinite series. Taylor series. Conic sections.
MATH2203 Lines and planes in 3-space. Vectors, functions of several variables, partial derivatives, multiple integrals, line integrals, vector analysis.
MATH2255 Logic, sets, functions, algorithms. Integers, induction and recursion. Relations, posits, equivalence relations, digraphs and matrix representations. Boolean algebra, applications to logic, Boolean identities, Boolean functions, minimization of circuits. Graphs. Trees.
MATH3210 A study of the integers: prime numbers, unique factorization, congruence, theorems of fermat and Euler, quadratic recriprocity, Diophantine equations, applications to cryptography and coding.
MATH3220 Vector spaces and linear transformations; systems of linear equations, bases, matrix representations of linear transforma- tions, matrix algebra, eigenvalues and eigenvectors, determin- ants, canonical forms, inner product spaces.
MATH3225 Groups, cyclic groups, subgroups, product and quotient groups, homomorphisms and isomorphisms. Rings, integral domains and fields.
MATH3231 The real number system, sequences and series, functions and continuity, differentiability, the Riemann integral, sequences and series of functions.
MATH3232 A survey of functions od several variables, multiple integrals, vector calculus, line integral, surface integral, and Green's and Stokes theorem
MATH3303 This course introduces students to the basic theory of probability. Both discrete and continuous probabilistic models are used to solve problems. Concepts and techniques from discrete math, such as Boolean Algebras are used in discrete cases. Differentiation and integration techniques are used in continuous cases. Students get familiar with common discrete distributions; binomial, geometric and Poisson. Continuous distributions covered include: normal, exponential, gamma and chi-squared. Students also learn how to calculate means, variances and moment generating functions.
MATH3305 This course exposes students familiar with the basic theory of probability to a few more advanced areas of probability and one special area of statistical analysis. The probabilistic areas include multivariate probability distributions and functions at random variables. The statistical component covers linear models, including both simple and multiple linear regression analysis.
MATH3306 Arrangements selections and distributions, generating functions, partitions and recurrence relations. Inclusion-exclusion principle. Graph models and isomorphisms. Planarity. Euler and Hamilton circuits. Graph coloring. Trees and graph algorithms. Applications, particularly to computer science.
MATH3309 Numerical solution of problems in analysis using the computer interpolation approximation, numerical integration and differentiation, solution of nonlinear equations and differential equations.
MATH3318 First order linear differential equations, linear differential equations with constant coefficients, variation of parameters, undetermined coefficients, Laplace transforms, solutions in terms of power series, numerical solutions with predictor- corrector and Runge-Kutta methods.
MATH3331 The Axiomatic approach to Euclidean and non-Euclidean geometry. Affine, projective, inversive, hyperbolic and spherical geometries according to Felix Klein's Erlangen Program.
MATH3335 Analytic functions. Cauchy's integral theorem and consequences, calculus of residues, entire and meromorphic functions, conformal mapping.
MATH3371 Definition of systems. Input, output and state variables. Continuous and discrete dynamical systems. Differential equations and their use in modeling. The CSMP language and its use. Spring
MATH4999 This course is a level assessment test for evaluating the breadth of knowledge in the major requirement and major elective courses. No class time is allocated for this course. The test is administered once every semester.
PHYS2003 A calculus-based course for students majoring in physics and other sciences. The first semester covers mechanics, heat and sound; the second semester covers electricity, magnetism, light and atomic physics. Fall, Spring
PHYS2004 A calculus-based course for students majoring in physics and other sciences. The first semester covers mechanics, heat and sound; the second semester covers electricity, magnetism, light and atomic physics. Fall, Spring
PHYS2013 LAB: associated with PHYS 2003 - General Physics with Calculus I
PHYS2014 LAB: associated with PHYS 2004 - General Physics with Calculus II