Math 181 Spring 2007 Lecture Progress


Week 1
1/17/07 Handed out syllabus. What is math? Logic is the math of reasoning critically. Inductive (oranges) vs. Deductive (All mammals have hair, etc.) Logic. Defitions of proposition, argument.
1/19/07 Intro deductive logic. Universal and Existential statements. Proving and disproving each. Counterexamples. Negating existential and universal statements. Inheritance. Validity & soundness.
Week 2
1/22/07 Reviewed validity and soundness.Valid = when all the premises are true, the conclusion is true. Sound = valid+ all true premises. Example of a valid statement with all false premises and a true conclusion. Example of invalid statement with all true premises and true conclusion. Filled in rules of inference sheet. Fallacy of affirming the conclusion. Fallacy of Denying the hypothesis. Connectives/logical symbols ("shorthand") for and, or, not, implies and if and only if. Started to work in groups on blue logic worksheet (the pdf itself is not blue,sadly) and logic connectives worksheet .

Announcements:
1/24/07 Another way to remember the truth-value rules for compound propositions (those that are made up of simpler propositions and connectives, e.g. "p and q", "p or q", etc.) - "and" is like multiplication (if true=1 and false=0) and "or" is like funny addition where 1+1 =1. Also, "p->q" should feel like the validity -- an argument isvalid if whenever the premises are true, the conclusion is true. "p->q" is false only when p (the premise) is true and it's conclusion,q, is false. Formal arguments -- reasoning backwards vs. flailing wildly. Worksheet (started in on it. BRING IT FRIDAY!) REMINDER: Quiz friday!
Also, if it helps, here are my (perhaps less than perfectly legible) notes.
1/26/07 Formal arguments, part II. Quiz 1. Quiz 1 solution
Week 3
1/29/07 Logic Puzzles: Knights & Knaves, Rosen #60(a) p21.
1/31/07 Chapter 2 PIL - Definitions and examples: sample-to-sample, sample-to-pop, pop-to-sample, testimony, inference to plausible explanation, some probability, decision theory.
2/2/07: Began Chapter 3 PIL - Gambler's Fallacy. Fairness = lack of bias +...? Def of bias. Quiz2. Quiz 2 solution
Week 4
2/5/07 Finished Chapter 3 PIL. Gambler's Fallacy. Fairness = lack of bias + independence. Gambler fallacious because he said the roulette wheel is fair, and then also reasoned as if it spins were dependent. Example of unbiased, dependent (coin trick where everytime you flip H it's followed by T -- H & T each show up half the time, but this is not a fair setup). Can have: (NOTE: know/be able to give examples of the above for the quiz). 6/49 Lottery.
2/7/07 Sections 4.1 & 4.3: Intro to Probability. Definitions of experiment(what was previously a "chance setup") , event (subset of possible outcomes). If all your outcomes in your event are equally likely, then
P(E) = (# outcomes resulting in E)/(total # outcomes)

Examples. How to find the probability of something "not" happening, knowing the probability of something happening (P(E) + P(not E) = 1, so P(not E) = 1-P(E)). Addition Rule of Probability -- problem of double counting. P(A or B) = P(A) + P(B) - P(A and B). Pictoral interpretation with a venn diagram. Collected homework.
2/9/07 Review & Conditional Probability. Quiz 3. quiz 3 solution
Week 5
2/12/07 Conditional Probability; all the proabability rules (on a version of this sheet.)
2/16/07 Conditional Proabability w/diagrams & Bayes' Rule. Quiz 4. Quiz 4 solution.
Week 6
2/19/07 Conditional Probability, Bayes' rule. False positives. Worked Probability Worksheet in class -- due for homework on Wednesday. Key for Probability Worksheet
2/21/07 Review
2/23/07 Midterm 1. Midterm 1 key
Week 7
2/26/07 Some discussion about the exam. Counting, tree diagrams, permuations & combinations
2/28/07The birthday problem; combinations and permutations in probability.
3/1/07 Graphs. Graphs a set of vertices and a relation-se. Different ways of drawing graphs. Quiz 5. Quiz 5 soln
Week 8
3/5/07 Graphs. Circuits. Complete graphs. Hamiltonian circuits. Travelling salesman problem. Nearest Neighbor Algorithm. Assigned homework.
3/7/07 Finding min cost hamiltonian circuit by listing. Number of hamiltonian circuits on a complete graph with n verices is (n-1)!/2. Showed this for n=3 and n=4. 3/9/07 Sorted edges algorithm. Quiz 6. Quiz 6 soln
Week 9
3/12/07 Trees. Forests (a graph where each connected component is a tree). Spanning trees. Kruskal's algorithm. Planarity. Euler's formula.
3/14/07 Planarity. Graph coloring.
3/16/07 Graph coloring. Quiz 7. Quiz 7 soln
SPRING BREAK
Week 10
3/26/07 Graph coloring. NOTE: MIDTERM 2 IS THIS FRIDAY. Handouts:
3/28/07REVIEW FOR EXAM2
3/30/07EXAM2. Exam2 Key
Week 11
4/2/07 Integers, primes, factors/divisibility. a|b means "a divides b", i.e. a is a factor of b. The sieve of Eratosthenes. Division Algorithm. Clock/modular arithmetic.Turing's Bicycle. Handed back exams and pages for homework. Assigned homework.
4/4/07 Modular Arithmetic & Turing's Bicycle.
4/6/07 Modular Arithmetic, Turing's Bicycle. Shift codes. Quiz 8. Quiz 8 Solution.
Week 12
4/9/07 Shift codes, Affine Ciphers -enciphering and deciphering. worksheet.
4/11/07 Affice Cipher Decoding, Hill cipher encoding.
4/13/07 Hill cipher decoding. Quiz 9 . Quiz 9 Solution.
Week 13
4/16/07 Hill Cipher decoding & RSA encoding. Worked on Hill Cipher wksheet and RSA worksheet
4/18/07 Hill Cipher decoding, RSA encoding, exponents in modular arithmetic and Euclidean Algorithm.
4/20/07 Euclidean Algorithm, & inverses. Quiz 10 . Quiz 10 Solution.
Week 14
4/23/07 Infinities
4/25/07 Exam Review
4/25/07 Exam 3. Exam 3 Key