David Dumas
University of Illinois at Chicago
Spring 2013
Triomino tilings of an 8x8 grid with one square removed. |
Meeting time | MWF 10:00 - 10:50am in Taft Hall 316 |
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Instructor | David Dumas (ddumas@math.uic.edu) |
Office hours | Monday 11-12 and Wednesday 12:30-1:30 in SEO 503 |
TA | Hexi Ye (hye4@uic.edu) |
TA Office Hours |
Monday 5-6pm and Friday 1-2pm in the MSLC Monday and Wednesday 12-1pm in SEO 401 |
Note: Math 215 help is available in the MSLC (SEO 430) from 8am to 6pm every weekday during the semester. | |
CRN | 34246 |
Textbook |
P. Eccles, An Introduction to Mathematical Reasoning Cambridge University Press, 1998. ISBN: 0521597188 |
Homework Policy | Weekly homework will be collected in class and graded. The two lowest grades will be dropped when computing your overall homework grade. |
Late homework is not accepted. | |
Clarity is essential. All solutions must be written in complete grammatical sentences. Submitted work must be legible (clearly hand-written or typed) and there should be no extraneous marks, symbols, or words on the pages except for your solution. Your grade will reflect both the mathematical correctness and the clarity of your writing. | |
You may discuss the homework problems with other students, but you must write your solutions independently. |
We will cover most of parts I–IV and some of part V in the textbook. Details can be found in the weekly schedule below.
Exam 1 | Friday, March 1 | In class |
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Exam 2 | Friday, April 5 | In class |
Final Exam | Friday, May 10, 10:30am-12:30pm | Location TBA |
Homework | 15% |
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Exam 1 | 25% |
Exam 2 | 25% |
Final Exam | 35% |
Week 1 | Statements, connectives, truth tables, negation, implication. Read Chapters 1 and 2. |
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Week 2 | Direct proofs, axioms for groups and for ordered fields. Read Chapter 3. |
Week 3 | Proof techniques: cases, contrapositive, contradiction. Examples. Read Chapter 4. |
Week 4 | Proof by induction, Fibonacci numbers. Read Chapter 5. |
Week 5 | Sets, subsets, equality, power set, union, intersection, difference, complement. Read Chapter 6. |
Week 6 | Cartesian product, quantifiers, alternation of quantifiers, functions. Read Chapter 7. |
Week 7 | Functions, graphs, composition, sequences. Read Chapter 8. Exam 1 on Friday. |
Week 8 | Injective, surjective, bijective functions, inverse functions. Read Chapter 9. |
Week 9 | Images and inverse images, partitions, equivalence relations. Read Chapter 22. |
Week 10 | Counting finite sets, inclusion-exclusion and pigeonhole principles. Read Chapters 10 and 11. |
Spring break | |
Week 11 | Counting for finite sets: subsets, functions, injections, surjections. Read Chapter 12. Exam 2 on Friday. |
Week 12 | Binomial coefficients and the binomial theorem. More on Chapter 12. |
Week 13 | Infinite sets, denumerable sets, countability of the rationals, uncountability of the reals. Read Chapter 14. |
Week 14 | Unions of countable sets, transcendental numbers, division theorem, Euclid's algorithm. Read Chapters 15 and 16. |
Week 15 | GCD and integer linear combinations, linear diophantine equations. Read Section 17.1 and Chapter 18. |