MAT1313

Topics List

Week #	Sections	Topics	Prerequisite Skills	Student Learning Outcomes
1	1.1 & 1.2	Propositional Logic	–	Recognize propositional formulas built from atoms using connectives. Correctly interpret propositional formulas using truth tables.
2	1.3 & 1.4	Tautologies and Deductions Quantifiers	Propositional Logic	Establish whether a propositional formula is a tautology. State De Morgan's Laws of logic. Recognize conditional tautologies as laws of deduction. Express conditionals in disjunctive form. Express the negation of a conditional in conjunctive form. Identify the direct and contrapositive forms of a conditional. Recognize the non-equivalence of a conditional and its converse. Recognize a biconditional as the conjunction of a conditional and its converse. Identify the domain of interpretation of a quantified statement. Correctly interpret quantified statements. Correctly negate quantified statements.
3	1.5 & 1.6	Sets Set Operations Introduction to proofs of universal statements in set theory Disproving universal statements via counterexamples	Tautologies and Deductions Quantifiers	Recognize and interpret set equality and set inclusion. Recognize set operations and state their formal definitions. Recognize formal proofs as processes of logical deduction of conclusions from assumptions. Prove basic universal statements pertaining to set inclusion and set operations. Correctly identify false universal statements in set theory and disprove them with appropriate counterexamples. Correctly use propositional and quantified tautologies as deductive laws.
4	2.1	Divisibility of integers The Division Algorithm	Proofs and Counterexamples Propositional Logic Quantifiers	Recognize the notion of integer divisibility via its formal definition, examples and counterexamples. Correctly state and apply the Division Algorithm of integers. Prove basic facts pertaining to divisibility and the division algorithm.
5	2.2 & 2.3	The Extended Euclidean Algorithm. Linear Diophantine equations in two variables.	Divisibility of integers. The Division Algorithm.	Express the GCD of two integers as a linear combination thereof. Solve integer linear equations mu+nv=a.

Course Catalog

MAT 1313. Algebra and Number Systems. (3-0) 3 Credit Hours.

Corequisite: MAT1214. Basic logic and proofs. Properties of integer numbers, mathematical induction, the fundamental theorem of arithmetic, the infinitude of primes, modular arithmetic, rational and irrational numbers, complex numbers, functions, polynomials, and the binomial theorem. Generally offered: Fall, Spring. Course Fees: LRS1 $45; STSI $21.