Difference between revisions of "MAT1313"

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(Improvements to Week 4)
(Reshuffle material in weeks 1-4.)
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==Course Catalog==
 
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[https://catalog.utsa.edu/undergraduate/sciences/mathematics/#courseinventory MAT 1313. Algebra and Number Systems]. (3-0) 3 Credit Hours.
 
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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.
 
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==Topics List==
 
==Topics List==
  
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2
 
2
 
|| <!-- Sections -->
 
|| <!-- Sections -->
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1.2
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1.3 & 1.4
 
||  <!-- Topics -->
 
||  <!-- Topics -->
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Tautologies and Deductions
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* Tautologies and Deductions
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* Quantifiers
 
||  <!-- Prereqs -->
 
||  <!-- Prereqs -->
 
* Propositional Logic
 
* Propositional Logic
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* Establish whether a propositional formula is a tautology.
 
* Establish whether a propositional formula is a tautology.
 
* State De Morgan's Laws of logic.
 
* State De Morgan's Laws of logic.
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* Recognize conditional tautologies as patterns of deduction.
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* Recognize conditional tautologies as laws of deduction.
 
* Express conditionals in disjunctive form.
 
* Express conditionals in disjunctive form.
 
* Express the negation of a conditional in conjunctive form.
 
* Express the negation of a conditional in conjunctive form.
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* Recognize the non-equivalence of a conditional and its converse.
 
* Recognize the non-equivalence of a conditional and its converse.
 
* Recognize a biconditional as the conjunction of a conditional and its converse.
 
* Recognize a biconditional as the conjunction of a conditional and its converse.
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|-  <!-- START ROW -->
 
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| <!-- Week# -->
 
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3
 
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|| <!-- Sections -->
 
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1.3, 1.4 & 1.5
 
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||  <!-- Topics -->
 
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* Quantifiers
 
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* Sets
 
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* Set Operations
 
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||  <!-- Prereqs -->
 
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* Propositional Logic
 
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||  <!-- SLOs -->
 
 
* Identify the domain of interpretation of a quantified statement.
 
* Identify the domain of interpretation of a quantified statement.
 
* Correctly interpret quantified statements.
 
* Correctly interpret quantified statements.
 
* Correctly negate quantified statements.
 
* Correctly negate quantified statements.
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* Recognize and interpret set equality and set inclusion.
 
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* Recognize set operations and state their formal definitions.
 
 
|-  <!-- START ROW -->
 
|-  <!-- START ROW -->
 
| <!-- Week# -->
 
| <!-- Week# -->
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4
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3
 
|| <!-- Sections -->
 
|| <!-- Sections -->
 
1.5 & 1.6
 
1.5 & 1.6
 
||  <!-- Topics -->
 
||  <!-- Topics -->
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Introduction to Proofs and Counterexamples
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* Sets
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* Set Operations
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* Introduction to proofs of universal statements in set theory
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* Disproving universal statements via counterexamples
 
||  <!-- Prereqs -->
 
||  <!-- Prereqs -->
 
* Tautologies and Deductions
 
* Tautologies and Deductions
 
* Quantifiers
 
* Quantifiers
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* Sets
 
−
* Set Operations
 
 
||  <!-- SLOs -->
 
||  <!-- SLOs -->
 +
* 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.
 
* Recognize formal proofs as processes of logical deduction of conclusions from assumptions.
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* 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).
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* Prove basic universal statements pertaining to set inclusion and set operations.
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* Prove basic results about set inclusion and set operations.
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* Correctly identify false universal statements in set theory and disprove them with appropriate counterexamples.
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* Correctly identify false universal statements and disprove them with appropriate counterexamples.
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* Correctly use propositional and quantified tautologies as deductive laws.
 
|-  <!-- START ROW -->
 
|-  <!-- START ROW -->
 
| <!-- Week# -->
 
| <!-- Week# -->
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5
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4
 
|| <!-- Sections -->
 
|| <!-- Sections -->
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2.1
 
||  <!-- Topics -->
 
||  <!-- Topics -->
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* Divisibility of integers
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* The Division Algorithm.
 
||  <!-- Prereqs -->
 
||  <!-- Prereqs -->
−
 
+
* Proofs and Counterexamples.
 +
* Propositional Logic.
 +
* Quantifiers.
 
||  <!-- SLOs -->
 
||  <!-- SLOs -->
−
 
+
* Recognize the notion of integer divisibility via its formal definition, examples and counterexamples.
 +
* Formally state the Division Algorithm of integers.
 +
* Prove basic facts pertaining to divisibility and the division algorithm.
 
|-
 
|-
 
|}
 
|}
 +
==Course Catalog==
 +
[https://catalog.utsa.edu/undergraduate/sciences/mathematics/#courseinventory 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.

Revision as of 16:48, 5 November 2021

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.
  • Formally state the Division Algorithm of integers.
  • Prove basic facts pertaining to divisibility and the division algorithm.

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.

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