Handouts
Math 300
2026 Spring

* The symbol * means not handed out in class; however, you should read on the internet.
Also, posted solutions usually are not distributed in class.

Group Work  and  Extra Exploration Activities

• §1.2 Lemma POO's friends 
• §3.1 Division Algorithm -vs- Congruence  (soln)
• §3.1 Congruence: transitivity and modulo arithmetic  (soln)
• §4.1 Induction 

Course Handouts   (HO)

1. Ch1: Intro to Writing Proofs   (summary) (statements and conditional statements, constructing direct proofs, divison algorithm, defs.)
2. §1.1: Class Example. statements.   (statement)
3. §1.2: Pascal's triangle (and binomial theorem)*   (algbra review of fast way to expand (x+y)ⁿ for a natural number n).
4. §1.2: Class Example. distance   (distance/quadrant)
5. §1.3: "IF ≠ IS" mistake
6. Ch2: Logical Reasoning   summary/packet, which includes:
   • §2.1: Statements and Logical Operators
   • §2.1: Contrapositive and Converse  (important class example)
   • §2.2: Logically Equivalent Statements
   • §2.3: Open Sentences and Sets
   • §2.4: Quantifiers and Negations
7. §2.1: Truth Table Practice Exercises (with solutions)*
8. §2.6: Ch 2 Practice ERs   (soln*)
9. Ch 3: Methods of Proofs.   summary/packet, which includes:
   • Ch3: Methods of Proofs   (chapter summary)
   • §3.1 Class Example. ER 3.1.8b divides vs congruent   (soln)
   • §3.2: Biconditional Sample Proofs
   • §3.4: Proof by Cases. Class Example using cases with the Division Algorithm  3| (n³ - n)
10. §3.6: Ch 3 Practice ERs   (soln)
11. Ch4: Math Induction  (summary and writing guidelines)
12. Ch4: Induction Examples   (soln)
13. Ch4: Induction Practice Problems   (soln)
14. §5.0: Set Theory Transition

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