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College Algebra for STEM (C-ID Math 151) or Precalculus (C-ID Math 155) or Precalculus and Trigonometry (sequence course)

1. Formal logic including statements, symbolic representation, tautologies, propositional logic, quantifiers, predicates, and validity, predicate logic, and logic programming;
2. Proofs, recursion, and analysis of algorithms including proof techniques, proof by induction, proof of correctness programming, recursive definitions, recurrence relations, and analysis of algorithms;
3. Sets, combinatorics, probability, and number theory including counting, principle of inclusion and exclusion; Pigeonhole Principle, permutations and combinations, and Binomial Theorem;
4. Relations, functions, and matrices including relations and databases, modular arithmetic;
5. Graphs and trees including graphs and their representations, trees and their representations, decision trees, and Huffman Codes;
6. Graph algorithms including directed graphs and binary relations; Warshall’s algorithm, Euler Path and Hamiltonian Circuit, shortest path and minimal spanning tree, traversal algorithms, and articulation points and computer networks;
7. Boolean Algebra and computer logic including Boolean algebra structure, logic networks, and minimization; and
8. Modeling arithmetic, computation, and languages including algebraic structures, finite-state machines, and formal languages.

Upon successful completion of the course, students will be able to:

1. Use recursion to analyze algorithms and programs;
2. Write proofs using symbolic logic and Boolean Algebra;
3. Use sets to solve problems in combinatorics and probability theory;
4. Apply matrices to analyze graphs and trees; and
5. Use finite state machines to model computer operations.

Tests, examinations, homework or projects where students demonstrate their mastery of the learning objectives and their ability to devise, organize and present complete solutions to problems.

A college level textbook supporting the learning objectives of this course.