Class Diary for M307, Spring 2009, Jochen Denzler
Introduction to Abstract Mathematics (Hons)
Wed Jan 07:
Instead of an introduction: solving
some inequalities;
let's see how many
you get wrong despite honest attempt ;-)
Fri Jan 09:
Discussion of how to get them right, and how to write it up intelligibly, and
unambiguously.
Mon Jan 12:
More discussion on inequalities; sample sol'n and
hwk. Book up to 1.4
Wed Jan 14:
Ifs, quantifiers, negations.
Fri Jan 16:
Some exercises pg 8; Hwk: pg 8, #3 and 7def written; also prepare
until 1.24
Mon Jan 19:
MLK DAY
Wed Jan 21:
A sample proof about set equality; material through 1.36. Hwk: prepare
9ab,10,11 from page 13 for presentation on the
board. Solve these problems
(not in the book) in writing by Fri
Fri Jan 23:
Feedback on hwk from page 8. Presentation of hwk from page 13.
Hwk: Read to end of Ch 1.
Mon Jan 26:
Presentation of #10 from page 13. Problems 22.
page 17, #23 and 24c in writing; 26 and 28 presentation. Resubmit the
Jan 21 hwk by Wed also.
Wed Jan 28: Discussion of 26,28. Brief rmks re Venn diagrams.
Hwk: Prepare 29,31,32
Fri Jan 30:
Final problems of Chapter 1. A slightly differnt perspective on Venn diagrams.
Hwk: Read sec 1 of chapter 2 till Mon. Also written
homework due Mon.
Mon Feb 02:
more on proving set equalities; in particular pblm 23 Hwk: redo parto it as ping-pong
Wed Feb 04:
cartesian products; relations: semantics vs syntax
Fri Feb 06:
comments on interval hwk; Q&A re exam; discussion of early sectn 2
Mon Feb 09:
EXAM 1
Wed Feb 11:
(SL) pg24, 2ab. Equivalence relations. Modular examples. Hwk 2cd, 3a-c due
Mon
Fri Feb 13:
(SL) 4b-d presentation. Equivalence classes and partitions.
Mon Feb 16:
Example: Constructing fractions as equivalence classes of pairs of
natural numbers. Hwk 5abe, 9,10 due Fri
Wed Feb 18:
Exam back, and comments. Outline about construction of arithmetic with
fractions. Functions defined.
Fri Feb 20:
Functions; image, and inverse image.
Mon Feb 23:
Comments on returned hwk.
Theorems and counterexamples about images and inverse images.
Hwk: p33f, #1a-d,2,4ab,6b
Wed Feb 25:
Comments on hwk p 28 #9. Inverse functions started.
Fri Feb 27:
Inverse functions; one-to-one and onto.
Mon Mar 02:
Hwk discussions.
Wed Mar 04:
Class presentation on (g o f)-1 = f-1 o g-1.
Some hwk discussion.
Fri Mar 06:
Induction. Hwk: p44: 1,2,3,5
Mon Mar 09:
A formula for the Fibonacci numbers proved by induction. A brief sketch how
to *prove* strong induction, assuming weak induction.
Wed Mar 11:
existence of prime number decomposition proved by strong induction. Borderline
cases that enter in the wording `a product of primes': empty product = 1.
Fri Mar 13: Hwk: p46, numbers 10,11
Induction and Inequalities; including Bernoulli's inequality (1+x)^n >= 1+nx if
x > -1.
Mon Mar 16:
SPRING BREAK
Wed Mar 18:
SPRING BREAK
Fri Mar 20:
SPRING BREAK
Mon Mar 23:
pg 49f: Discussion #15,19. Hwk: pg 50 #16,28
Wed Mar 25:
questions concerning induction with inequalities; Binomial thm begun.
Fri Mar 27:
Sol'n p 50 #28 discussed. Binomial thm proved.
Mon Mar 30: EXAM 2
Wed Apr 01: Filed Axioms. Hwk: pg 60, numbers 1-3
Fri Apr 03: Consruction / definition of subtraction and dvision from the
field axioms. Order axioms. Hwk: think how to prove 1>0 directly from the
axioms. (Hint: use trichotomy property)
Mon Apr 06:
powers inductively defined; som exercises on order axioms.
Wed Apr 08:
power laws from axioms; absolute value. Hwk: pg 66, numbers 36,39
Fri Apr 10:
GOOD FRIDAY
Mon Apr 13:
some hwk discussion. Proof that there is no rational number whose square is 2.
Wed Apr 15:
Fri Apr 17:
Mon Apr 20:
EXAM 3
Wed Apr 22:
Fri Apr 24:
MON APR 27: STUDY DAY
Mon May 04: FINAL EXAM 10:15-12:15
(scheduled by university policy)
-------------------------------------------