Foundations
of Higher Mathematics 
Syllabus 
Evaluation Form 



Tentative schedule: 

Presentation
Topic Handouts 
Observational Checklist 











Week 
Topic 
Tuesday 9:3010:50 
Thursday 9:3010 
Thursday 1010:50 



31Jan 
Language of
proof 
Propositions 
Propositions & Quantifiers [1.11.3] 
Quantifiers [1.11.3] 



7Feb 
Sets 
Introduction to Set Theory [2.1] 
Set Operations [2.2] 
Group work 



14Feb 
Language of
proof 
Quantifiers & Methods of Proof [1.4] 
Group work 
Group work 



21Feb 
Mathemetical
Induction 
Induction proofs [3.1] 
Further Induction Results [3.2] 
Group work 



28Feb 

Further Induction Results [3.2] 
Number Theory [3.45] 
Group work 



7Mar 
Number Theory 
Number Theory [3.45] 
Number Theory [3.45] 
Group work 



14Mar 
Relations and
Congruence 
Number Theory [3.45] 
Relations & Graphs [4.1&2] 
1st Student Presentation day 



21Mar 

Relations & Graphs [4.1&2] 
Equivalence Relations [4.3] 
Group work 



28Mar 
More Number Theory 
Congruence [4.5] 
Congruence [4.5] 
2nd Student Presentation day 



4Apr 
Functions 
Functions as Relations [5.1] 
Images and Inverse Images [5.5] 
Group work 



11Apr 

Spring 
Break 
!!! 



18Apr 
Elementary
Analysis 
Sequences and Convergence [9.1] 
Subsequences [9.2] 
3rd Student Presentation day 



25Apr 

Limits of Functions [9.3] 
Continuity [9.4] 
4th Student Presentation day 



2May 
Combinatorics 
Sum and Product rules [6.1] 
Pigeonhole Principle [6.2] 
Group work 



9May 

Binomial Theorem [6.3] 
Graphs [6.4] 
5th Student Presentation day 



16May 

catch up 
catchup 
Group work 



23May 


FINAL at 10:15 












Week 
Topic 
Assignment: 
Remarks 




31Jan 

Complete
Survey 
First Journal due Monday via email. 




7Feb 
Language of proof 
F&P # 6,13,27,39,41,42. 





14Feb 
Sets 
F&P Chap 2 # 1,10,15,17,18,19. 





21Feb 
Language of proof 
F&P Chapter 1 # 43, 59, 67, 73(a), 73(b),
73(c)and (d), and supplemental problem (see right) 
supplemental
problems for homework 3 click here! 




28Feb 
Induction 
F&P Chap 3: # 1d, 1k, 1m, 1q, 5, 8, 15,19. 
See new hints in induction handout (latest version!) 




7Mar 
Induction 
F&P Chap. 3: 20, 25, 28, 35, 36, 39 (do not
hand in), 40, 52. 
See new hints in induction handout (latest version!) 




14Mar 
Number Theory 
F&P Chapter 3 # 84, 94, 95, 101,103, 111,112
118. 
Click
here for homework hints 




21Mar 
Relations 
F&P Chapter 4 # 10, 11,13,19,20,25,34. 





28Mar 
Equivalence Relations 
F&P Chapter 4 # 35, 37, 40, 42, 65. 





4Apr 
Congruence 
F&P Chapter 4 # 66, 67,68,70 (hint: induction on
m),73,75 (read Chinese Remainder Theorem, Thm 4.14), 81. 





18Apr 
Functions 
See end of handout on functions 





25Apr 
Functions 
F&P Chapter 5 # 67, 69, 73 and problem 8 from
last week's homework. 





2May 
Analysis 
See Homework I on Analysis in handout 
Practice
Final 
Other
320's Midterm from this term 



9May 
Analysis 
See Homework II on Analysis in handout second to
last page of most recent version on the web (corrected 5/4/06) and fill out
the survey to the left and return it to me. 
Department
Survey 




16May 
Review 
Do the practice final & Midterm. Also fill out
the two surveys to the right and return it to the secretary in the math
department. 
Evaluation
Form 
Study
skills survey 


































































































































































































































































































