MATH 347: Fundamental Mathematics

Fall 2008, section X1

MWF, 12-12:50 PM, Altgeld 343

Tentative schedule

Readings should be completed by the start of class on the dates listed below.
Similarly, homework is due at the start of class on the assigned dates.

Week beginning Assigned reading Assigned homework Description
August 25, 2008 Chapter 1 (by Wed, Aug. 27)
Chapter 2 (by Fri, Aug. 29)
1.7, 1.13, 1.14, 1.15, 1.16, 1.21, 1.22, 1.50
due Wed, Sept. 3
The real numbers
September 1, 2008 none 2.2, 2.4, 2.9, 2.16, 2.21, 2.31, 2.32, 2.37, 2.40(a) and these supplementary problems
(this list is now final).
Note that there is a typo in the hint for Exercise 2.31; it refers you to Remark 2.88, which is not very kind since as far as I can tell it doesn't exist. Please see Remark 2.34 instead.
due Wed, Sept. 10

Note on the supplementary problems: These problems assume knowledge of the axioms for a field as well as the order axioms (the definition of a positive set). For the field axioms, please use the list given here. This list is updated from the handout I gave you in class. (It includes as axioms properties that would have required proof if we used the previous list -- in other words, this new list should make your life easier!) The order axioms are the same as those given in class; if you didn't take notes, these axioms constitute Definition 1.40 on p.16 of our book.

Real numbers, ctd., and mathematical statements
September 8, 2008Chapter 3 (by Mon, Sept. 8) 3.1, 3.11, 3.15, 3.22, 3.25, 3.29, 3.35, 3.44

Extra credit problem (to be turned in to me, not the grader; it must be written/typed on a separate sheet of paper):
(a) Show that if n is a natural number and n > 1, then n-1 is also a natural number.
(b) Use the result of (a) to show that the set of integers Z is closed under addition and multiplication: that is, if m and n are integers, then so are m+n and mn.

Induction
September 15, 2008Chapter 4 (by Mon, Sept. 15)
Chapter 5 (by Fri, Sep. 19)
the HW assignment (due Wed, Sept. 24) is now posted here Bijections and cardinality
September 22, 2008 No assigned reading for this week A list of practice problems for Exam 1 is now posted here
Solutions to HW number 4 are now posted here (note that for ease of typesetting, to indicate a difference of two sets I use the symbol "\" where the book would have "–" in other words, I write "A\B" and not "A–B")

First exam (=celebration of learning)
September 29, 2008 No assigned reading for this week 5.18, 5.23, 5.27, 5.28, 5.30, 5.31, 5.37, 5.41, 5.42
(due Friday, Oct. 10)

Intro to combinatorics
October 6, 2008 Chapter 6 (by Friday, Oct. 10) the HW assignment (due Fri, Oct. 17) is now posted here Intro to number theory (divisibility)
October 13, 2008 no new assigned reading Divisibility ctd.
October 20, 2008 Chapter 7 (by Friday, October 24) A list of practice problems for Exam 2 is now posted here
Solutions to HW 6 are posted here
Modular arithmetic
October 27, 2008 no new assigned reading HW 7 (due Wednesday, November 5) is now posted hereModular arithmetic ctd.
November 3, 2008 Chapter 13 (by Wednesday, November 5) Introduction to real analysis
November 10, 2008 no new reading assigned HW 8 (due TBA) is now posted here Introduction to real analysis, ctd.
November 17, 2008 no new reading assigned Chapter 14 is not assigned reading, but it would be helpful as a written reference for our discussion of infinite series.
A list of practice problems for Exam 3 is now posted here
HW #8 solutions are now posted here
Introduction to real analysis, ctd.
December 1, 2008 Chapter 10 Exercises 10.1, 10.2, 10.8, 10.12, 10.15, 10.28, 10.29, 10.36, 10.37 The pigeonhole principle and the principle of inclusion-exclusion


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