Math 8 -
Transitions to
Higher Mathematics - Fall 2007
Professor: Alex Dugas my
homepage
Office: 6510 South Hall
Office Hours: W 10-12, F 2-3
Prerequisites: Math 3B (with a grade of C or better).
Text: Larry Gerstein. Introduction
to Mathematical Structures and Proofs. Springer-Verlag 1996.
Lecture: MWF
Section: You must sign up for and attend a discussion section as
well.
The section times and locations for this course are as follows:
The GSI for this course is Tom Howard. His office hours, in SH
6431L,
are:
Announcements:
Course Timetable (subject to change) |
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Date |
Topics |
Reading |
Homework |
Due Date |
|
F 9/28 |
|
Ch. 1.1 |
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Th 10/4 |
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M 10/1 |
Logical Connectives: Not,
And, Or. Truth Tables. |
Ch. 1.2 |
1.3: Ex. 1, 4 |
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W 10/3 |
Conditional
Propositions; Biconditionals; Converse. |
Ch. 1.3 |
1.3: Ex. 2, 8, 11c,d, 18a,d |
Th 10/11 worksheet solutions |
|
F 10/5 |
Contrapositive; Logical Equivalence; De Morgan's Laws. |
Ch. 1.5 |
1.5: Ex. 3, 4, worksheet (#'s 1, 3) |
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M 10/8 |
Direct Proofs. Arithmetic Review Sheet. |
Ch. 1.4 |
1.4: Ex. 2, 3a,b |
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W 10/10 |
Indirect Proofs. |
Homework 3 |
Th 10/18 Solutions |
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F 10/12 |
Proof by Contradiction. |
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M 10/15 |
Sets. Notation and
Definitions. |
Ch. 2.1 |
2.1: Ex. 2-5, 7 |
Th 10/25 Worksheet Solutions |
|
W 10/17 |
Set Builder
Notation. Set Equality. |
Ch. 2.1 |
worksheet |
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F
10/19 |
Midterm
1 |
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M 10/22 |
Quantifier Notation. |
Ch. 2.3 |
2.3: 1, 4a-c |
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W 10/24 |
Russel's Paradox. |
(Ch. 2.2) |
2.3: 2, 9 |
Th 11/1 |
|
F 10/26 |
Set Inclusion.
Subsets. |
Ch. 2.4 |
2.4: 1, 4, 7a, 9 |
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M 10/29 |
Set Operations.
Unions. Intersections. Complements. Venn Diagrams. |
Ch. 2.5 |
2.5: 1, 3, 6, 7 |
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W 10/31 |
Families of Sets indexed
by a set. Intersection, Union of indexed families of sets. |
Ch. 2.6 |
2.6: 2a-c, 6a-c |
Th 11/8 |
|
F 11/2 |
Ordered Pairs.
Cartesian products. |
Ch. 2.7, 2.8 |
2.7: 1, 2a,b, 8 2.8: 4a-c, e, 9 |
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M 11/5 |
Class Canceled! |
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W 11/7 |
Functions.
Functions as sets of ordered pairs/graphs or as diagrams.
Composition. |
3.1 |
3.1: 1, 2, 5, 7a,b |
Tu 11/20 |
|
F 11/9 |
Injective/One-to-One
Functions. Surjective/Onto Functions. Bijective Functions. |
3.2 |
3.2: 2, 3, 9 |
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M 11/12 |
Veteran's day: No Class |
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W
11/14 |
Midterm
2 |
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F 11/16 |
Composition of
Functions. Inverse Functions. |
3.3 |
3.3: 2, 7, 8, 11 |
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M 11/19 |
Cardinality of Sets.
Equipotent Sets. |
4.1 |
4.1: 3, 4a,b, 6 | Th 11/29 |
|
W 11/21 |
Finite and Infinite
Sets.
Pigeonhole principle. Countable and Uncountable Sets. Lecture Notes: pg. 1, pg. 2,
pg. 3 |
4.2 |
4.2: 4, 5a,c |
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F 11/23 |
Thangksgiving Holiday: No Class |
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M 11/26 |
Countable and Uncountable
Sets. (cont.) |
4.3 |
4.3: 1, 4, 7, (optional: 11) |
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W 11/28 |
Mathematical Induction. |
2.10 |
2.10: 1, 3, 6 |
Th 12/6 |
|
F 11/30 |
Induction (cont.).
Cardinality of Power Sets. |
2.10 |
2.10: 4, 9 |
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M 12/3 |
Strong Induction. Recursive Sequences. Fibonacci Numbers. | 2.10 |
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W 12/5 |
Binomial
Coefficients. Pascal's Triangle (not on final) |
(5.8) |
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F 12/7 |
Review. |
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Th 12/13 |
Final Exam - 8:00 - 11:00 am |
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