Mathematics

This course is the first in the three-course calculus sequence intended for majors in math, engineering, and physical sciences. The course covers elements of analytic geometry, derivatives, limits and continuity, differentiation of algebraic and trigonometric functions, and the definite integral. Application to the sciences are also covered.

Continuation of differential and integral calculus, including transcendental, and inverse functions. Techniques of integration, numerical integration, parametric equations, polar coordinates, sequences, power series and Taylor series. Primarily for mathematics, physical science, and engineering majors.

Vector valued functions, functions of several variables, partial differentiation, multiple integration, change of variables theorem, scalar and vector fields, gradient, divergence, curl, line integral, surface integral, Theorems of Green, Stokes and Gauss, applications.

Choose one course from List A below

Choose one course from List A below

Choose one course from List B below

Introduction to elementary differential equations, including first and second order equations, series solutions, Laplace transforms, and applications.

Introduction to linear algebra: matrices, determinants, systems of equations, vector spaces, linear transformations, eigenvalue, eigenvectors, and applications.

Introduction to structured programming and problem solving using the C++ language. Problem solving techniques, algorithm design, testing and debugging techniques, and documentation standards. C++ syntax: elementary operators, data types, control structures, user-defined and library functions, basic input/output, sequential files, arrays and structs. Appropriate for students with little or no programming experience, but comfortable using computers with modern GUI operating systems.

Object-oriented programming methods employed to design, program, test and document intermediate level problems. Includes strings and string objects, multidimensional arrays, pointers, dynamic allocation, classes, overloaded functions, inheritance and polymorphism, introduction to linked lists. Designed to satisfy Association of Computing Machinery (ACM) guidelines for CS I as required for Computer Science and related transfer majors.

Object-oriented programming methods employed to design, program, test and document intermediate level problems in the Java language. Overview of Java syntax, control structures, methods, I/O, strings, single and multidimensional arrays, recursion and exception handling. Abstract Data Types and Object-Oriented Programming principles including classes, information hiding, aggregation, inheritance, method overriding and polymorphism. Introduction to graphical user interfaces (GUIs) and applets using the javax.swing package. Dynamic allocation and de-allocation of memory; comparison of Java references with pointers in C++. Implementation and use of linked lists. Designed to satisfy Association of Computing Machinery (ACM) guidelines for CSI as required for Computer Science and related transfer majors.

Design and implementation of larger projects using object-oriented software engineering principles. Emphasis on definition and use of data structures. Includes specification of Abstract Data Types, recursion, dynamic memory allocation, stacks, linked lists, priority queues, graphs, binary trees, heaps, sorting and searching, algorithm analysis, hashing techniques, random access files.

Sets, relations and functions; logic, methods of proof, induction; combinatorics, discrete probability, recursion, and recurrence relations; graphs and trees; logic circuits; finite state machines. Designed for majors in mathematics and computer science.