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SYLLABUS AND HOMEWORK

Mathematics 2001
Spring 2016

Introduction to Discrete Mathematics

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Homework is due in class and must be stapled, with your name on it, to receive credit.

You may find the Mathematics Help Room (MATH 175) to be useful as a meeting point for discussing homework.

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Date	Topics covered	Reading	Homework Assignments
Monday January 11	Introduction	Hammack Chapter 1
Wednesday January 13	Introduction to LaTeX	If possible, bring a laptop with LaTeX installed (see the bottom of this page). We will use the following .tex and .bib files (which generate this .pdf).
Friday January 15	Introduction to sets Overview.		HW1: Due Friday January 15 Hammack Chapter 1 Exercises: Section 1.1: 2, 8, 18, 30, 38, 40.
Monday January 18	NO CLASS MLK		NO CLASS MLK
Wednesday January 20	Introduction to LaTeX continued.	If possible, bring a laptop with LaTeX installed (see the bottom of this page). We will use the following .tex and .bib files (which generate this .pdf).
Friday January 22	Sets continued: Venn diagrams, subsets, union, intersection, difference, complement.		HW 2: Due Friday January 22 Hammack Chapter 1 Exercises: Section 1.2: 2, 4, 8, 12, 18. Exercises on sets: 1.48, 1.49 on the following .pdf
Monday January 25	Sets continued: Products of sets, power sets, indexed sets, sets of numbers.
Wednesday January 27	Sets continued: Maps of sets.
Friday January 29	Introduction to linear algebra Vector spaces, subspaces, linear maps.	Read this .pdf on linear algebra	HW 3: Due Friday January 29 Hammack Chapter 1 Exercises: (5 points extra credit for typing in LaTeX.) Section 1.3: 2, 6, 12. Section 1.4: 2, 10, 14, 19. Section 1.5: 2, 4, 6. Section 1.6: 2. Section 1.7: 4,5,6. Section 1.8: 2, 11, 12. Not for credit: Exercises on sets on the following .pdf (Do not turn these in.)
Monday February 1	Introduction to logic Overview	Hammack Chapter 2
Wednesday February 3	Logic continued: Overview of proofs.
Friday February 5	Review		HW 4: Due Friday February 5 Hammack Chapter 2 Exercises: (5 points extra credit for typing in LaTeX.) Section 2.1: 2, 4, 6. Section 2.2: 2, 6. Section 2.3: 8, 10. Section 2.4: 4. Exercises 6.3-6.15 on linear algebra on the following .pdf
Monday February 8	Homework review
Wednesday February 10	Review
Friday February 12	MIDTERM I		MIDTERM I
Monday February 15	LaTeX review	If possible, bring a laptop with LaTeX installed (see the bottom of this page). We will use the following .tex and .bib files (which generate this .pdf).
Wednesday February 17	Logic continued: Statements, and or not, conditional statements, biconditional statements, truth tables, logical equivalence.
Friday February 19	Logic continued: Quantifiers, translating english into symbolic statements, negating statements, logical inference		HW 5: Due Friday February 19 Hammack Chapter 2 Exercises: (Must by typed in LaTeX.) Section 2.5: 4, 6, 8. Section 2.6: 4, 6. Section 2.7: 2, 4, 8. Section 2.9: 2, 3, 4, 5. Section 2.10: 2, 4, 10.
Monday February 22	Linear algebra continued: Proofs of some linear algebra statements.	Read the .pdf on linear algebra again
Wednesday February 24	Some techniques of proof Definitions (4.2), direct proof, mathematical writing (5.3), contrapositive proof.	Hammack Chapter 4 Hammack Chapter 5
Friday February 26	Review		HW 6: Due Friday February 26 Hammack Chapter 4-5 Exercises: (Must by typed in LaTeX.) Chapter 4: 1-10. Chapter 5: 1-5, 16-20. Not for credit: Exercises 6.17-6.25 on linear algebra on the following .pdf (Do not turn these in.)
Monday February 29	Techniques of proof continued: Proof by contradiction.	Hammack Chapter 6
Wednesday March 2	Techniques of proof continued: Proving non-conditional statements, proofs involving sets, disproof.	Hammack Chapter 7 Hammack Chapter 8 Hammack Chapter 9
Friday March 4	Review		HW 7: Due Friday March 4 Hammack Chapter 6-7 Exercises: (Must by typed in LaTeX.) Chapter 6: 2-8. Chapter 7: 19-21. Exercises 6.3-6.15 on linear algebra on the following .pdf
Monday March 7	Techniques of proof continued: Proof by induction.	Hammack Chapter 10
Wednesday March 9	Relations Reflective, symmetric, transitive,	Hammack Chapter 11
Friday March 11	Review		HW 8: Due Friday March 11 Hammack Chapter 8-10 Exercises: (Must by typed in LaTeX.) Chapter 8: 2, 6, 10-18. Chapter 9: 2, 4, 6, 8, 10, 12, 14. Chapter 10: 1-15. Exercises 6.17-6.25 on linear algebra on the following .pdf
Monday March 14	Homework review
Wednesday March 16	Review
Friday March 18	MIDTERM II
Week of March 21-March 25	SPRING BREAK		SPRING BREAK
Monday March 28	Functions	Hammack Chapter 12
Wednesday March 30	Functions continued: Composition, inverse, image, pre-image, injective, surjective, and bijective.
Friday April 1	Review		HW 9: Due Friday April 1 Hammack Chapter 11 Exercises: (Must by typed in LaTeX.) Section 11.0: 2, 4, 6. Section 11.1: 2, 6, 10. Exercises 6.3-6.15 on linear algebra on the following .pdf
Monday April 4	Functions continued:
Wednesday April 6	Equivalence relations
Friday April 8	Review		HW 10: Due Friday April 8 Hammack Chapter 12 Exercises: (Must by typed in LaTeX.) Section 12.1: 4, 6. Section 12.2: 5, 10. Section 12.3: 1, 2. Section 12.4: 2, 6, 10. Section 12.5: 2, 8. Exercises 6.17-6.25 on linear algebra on the following .pdf Not for credit: Section 12.6: 2, 4, 6, 8, 10, 12, 14. (Do not turn these in.)
Monday April 11	Equivalence relations continued: Partitions, quotients, universal properties.
Wednesday April 13	Partially ordered sets
Friday April 15	Review		HW 11: Due Friday April 15 Hammack Chapter 11 Exercises: (Must by typed in LaTeX.) Section 11.2: 2, 5, 11, 12. Section 11.3: 2, 4. Section 11.4: 4, 6. Exercises 6.3-6.15 on linear algebra on the following .pdf
Monday April 18	Partially ordered sets continued:
Wednesday April 20	Cardinality	Hammack Chapter 13
Friday April 22	Cardinality continued: Countability, comparing cardinality, Cantor--Bernstein--Schroeder Theorem.		HW 12: Due Friday April 22 Not for credit (do not turn these in): Hammack Chapter 13 Section 13.1: 4, 10. Section 13.2: 3, 9. Section 13.3: 4, 8, 10. Section 13.4: 1, 2. Exercises 6.17-6.25 on linear algebra on the following .pdf
Monday April 25	Homework review
Wednesday April 27	Review
Friday April 29	Review
Tuesday May 3	FINAL EXAM 1:30 PM - 4:00 PM ECCR 108 (Lecture Room)		FINAL EXAM

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I strongly encourage everyone to use LaTex for typing their homework. If you have a mac, one possible easy way to get started is with texshop. If you are using linux, there are a number of other possible ways to go, using emacs, ghostview, etc. If you are using windows, you're on your own, but I'm sure there's something online. Here is a sample homework file to use: (the .tex file, the .bib file, and the .pdf file). It is probably easiest to just look at the .tex file, and start to experiment. There is also the (Not so) short introduction to latex, which will answer most of your questions (although typing your question into your favorite search engine will probably work well, too). This site can help you find LaTeX symbols by drawing: http://detexify.kirelabs.org/classify.html. You may also want to try https://cloud.sagemath.com/ or https://www.sharelatex.com/ for a cloud version.