ma 225 -- Course review sheet 2001

For each item listed, you should

(a) Know all relevant definitions (compete sentences!)

(b) Know the standard notation

(c) Know how to tackle typical problems

(d) Know how to prove typical theorems

(i) how to get started

(ii) how to state conclusions

(iii) how to get from start to finish
 
 

I. Propositions

A. The 5 basic Connectives (~, Ú , Ù , ? , Û )

B. Terminology -- Necessary, Sufficient, iff, etc.

C. Proof Types -- Direct, Indirect, Contrapositive, Contradiction, iff

D. Quantifiers (" , $ , $ !) -- Translation from symbols to English and v.v. --

Proofs involving quantifiers.

E. Proofs using the method of Mathematical Induction

F. Propositions are sentences; sentences contain verbs and proper punctuation.
 
 

II. Sets

A. Basic Connectives (~, È , Ç )

B. Basic Relations (Î , Í , =)
 
 

III. Relations

A. Basics -- Definition, Domain, Range, Codomain, Digraphs

    1. Inverse and Composite Relations

IV. Functions

A. Basics -- Definition, Domain, Range, Codomain, Standard Functions from

Calculus, Special Functions (Identity, Characteristic, etc.)

B. Inverse and Composite Functions