Upon successful completion of the course, students will be able to: define and apply integration including definite integrals and its connection to area; calculate limits; calculate integration of logs, exponential functions, trigonometric functions and integrate by parts, integrate using partial fractions; solve problems involving area, volume, rectilinear motion and growth and decay; numerical methods for calculating integrals; and solve differential equations by separating variables.

Upon successful completion of the course, students will be able to: read, interpret and write presentations using logical mathematical symbols; write proofs of truth value of propositions, using inference rules and axioms of logic; use set theory to explain mathematical logic involving collections of objects as units; discuss the concept of algorithms as processes to solve problems;  solve a recurrence relation; tell whether a function is injective or subjective; define functions explicitly and recursively; calculate probabilities using counting rules, combinations and permutations; write proofs relating number of vertices and number of edges in a tree; write proofs related to connectedness of graphs; and find shortest path in a graph;show isomorphism.

Upon successful completion of the course, students will be able to: understand vectors and vector spaces; solve systems of linear equations; perform matrix arithmetic; solve equations involving matrices; define and use determinants, minors, cofactors, classical ad joints, eigenvalues, and eigenvectors of matrices, canonical form of matrices, and invariant subspaces; show that a set of vectors is linearly independent and/r spanning a vector space; define and find the dimension; define and find the rank and nullity of a matrix; find the row space, column space and null space of a matrix; use inner and cross products and the scalar triple product.