for 12 classes
Discrete Math Part I: Logic
Completed by 2 learners
Ages 13-17
Live Group Class
Average rating:
5.0
Number of reviews:(11 reviews)
Live video meetings
2x per week, 6 weeks
1-18 learners per class
120 min
What's included
12 live meetings
24 in-class hoursClass Experience
Course Description Topics include Formal Logic: Inquiry problems, connectives and propositions, truth tables, logical equivalences; Propositional Logic: Tautologies and contradictions, derivation rules, proof sequences, forward-backward; Predicate Logic: Predicates, quantifiers, translation, negation, two common constructions; Logic in Mathematics: The role of definitions in mathematics, other types of mathematical statements, counterexamples, axiomatic systems; and Methods of Proof: Direct proofs, proof by contraposition, proof by contradiction. Prerequisites The class is taught with the assumption that the student has a strong understanding of Algebra. Calculator Although this is a Mathematics course, a calculator will be of little to no use for the topics and problems we will discuss. Purpose Discrete Mathematics is designed for prospective math/computer science majors as well as for students whose primary interest is engineering or the physical and social sciences. Discrete Mathematics Part I Course Schedule Class meets twice weekly Week 1: Formal Logic Lesson 1: Inquiry Problems/Connectives and Propositions Lesson 2: Truth Tables/Logical Equivalences Week 2: Propositional Logic Lesson 1: Tautologies and Contradictions/Derivation Rules Lesson 2: Proof Sequences/Forward-Backward Week 3: Predicate Logic Lesson 1: Predicates/Quantifiers Lesson 2: Translation/Negation/Two Common Constructions Week 4: Logic in Mathematics Lesson 1: The Role and Definitions in Mathematics/Other Types of Mathematical Statements Lesson 2: Counterexamples/Axiomatic Systems Week 5: Methods of Proof Lesson 1: Direct Proofs Lesson 2: Proof by Contraposition Week 6: Methods of Proof and Exam Lesson 1: Proof by Contradiction Lesson 2: Exam
Learning Goals
Student Learning Outcomes
The student will at least be able to demonstrate competency in:
1) Formal Logic
a. Contemplating and Solving Inquiry Problems
b. Identifying Statements, Connectives, and Propositions
c. Forming and Evaluating Truth Tables
d. Identifying, Understanding, and Proving Logical Equivalences
2) Propositional Logic
a. Identifying and Understanding Tautologies and Contradictions
b. Evaluating and Proving Tautologies and Contradictions with Truth Tables
c. Utilizing Equivalence and Inference Rules
d. Understand and Write Proof Sequences
e. Implement the Forward-Backward Approach to Devising Proof Sequences
3) Predicate Logic
a. Understanding Predicates and Quantifiers
b. Translating Between English Statements and Predicate Logic
c. Negating Quantified Statements
d. Recognizing Forms of Two Common Constructions
4) Logic in Mathematics
a. Understanding of Role of Definitions in Mathematics
b. Identifying the Difference Between Axioms, Theorems, and other Types of Mathematical Statements
c. Citing Counterexamples
d. Understanding Axiomatic Systems
5) Methods of Proof
a. Reading and Writing Direct Proofs
b. Understanding and Utilizing Proofs by Contraposition and ContradictionOther Details
External Resources
Learners will not need to use any apps or websites beyond the standard Outschool tools.
Meet the teacher
Joined March, 2021
5.0
11reviews
Teacher expertise and credentials
I am an HSI STEM Instructor and Supplemental Instructor at the Rowan College of South Jersey, with specialties in Mathematics, Engineering, and Computer Science.Reviews
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