MAT1313

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.

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	1.2	Tautologies and Deductions	Propositional Logic	Establish whether a propositional formula is a tautology. State De Morgan's Laws of logic. Recognize conditional tautologies as patterns 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.
3	1.3, 1.4 & 1.5	Quantifiers Sets Set Operations	Propositional Logic	Identify the domain of interpretation of a quantified statement. Correctly interpret quantified statements. Correctly negate quantified statements. Recognize and interpret set equality and set inclusion. Recognize set operations and state their formal definitions.
4	1.5 & 1.6	Introduction to Proofs and Counterexamples	Tautologies and Deductions Quantifiers Sets Set Operations	Recognize formal proofs as processes of logical deduction of conclusions from assumptions. Identify strategies for proofs (direct or contrapositive proofs of conditionals; use of cases when given alternative assumption, or when proving simultaneous conclusions; proofs of equivalences; proofs by contradiction). Prove basic results about set inclusion and set operations. Correctly identify false universal statements and disprove them with appropriate counterexamples.
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