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
|
–
|
- Ability to recognize propositional formulas built from atoms using connectives.
- Ability to 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
- Introduction to proofs.
|
- Propositional Logic
- Tautologies and Deductions
|
- 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
|
Proofs and Counterexamples
|
- Recognize a formal proof as a process of logical deduction of conclusions from assumptions.
- Prove basic results about set inclusion and set operations.
|
|
