Math 60 is an honors version of Math 20. It covers the material of Math 20 but in more depth and from a much more theoretical perspective, with an emphasis on formal proofs. Several additional topics (including generating functions, branching processes, random walks) are added.
Math 20 Course Description: Our capacity to fathom the world around us hinges on our ability to understand quantities which are inherently unpredictable. Therefore, in order to gain more accurate mathematical models of the natural world we must incorporate probability into the mix. This course will serve as an introduction to the foundations of probability theory. Topics covered will include some of the following: discrete and continuous random variables, random vectors, multivariate distributions, expectations; independence, conditioning, conditional distributions and expectations; strong law of large numbers and the central limit theorem; random walks and Markov chains.
Lectures: 
M, W, F,  11:30am  12:35pm 
Kemeny 007  Tu,  12:15pm  1:05pm (Xhour) 
Office Hours: 
Monday,  4:00pm  5:00pm 
Kemeny 320  Tuesday,  3:00pm  4:00pm 
Thursday,  10:00am  11:00am 
Graduate TA: 
Laura Petto  
Office Hours:  Tuesday,  1:00pm  2:00pm 
Kemeny 241  Friday,  2:00pm  3:00pm 
Tutorial:  Monday,  6:30pm  8:00pm 
Kemeny 105 
Weekly graded homework assignments, posted above. Daily suggested homework from the textbook, not graded.
Quiz 1:  Tuesday, April 10 
Exam 1:  Tuesday, April 24 
Quiz 2:  Tuesday, May 8 
Final Exam:  Saturday, June 2 
Homework:  25% 
Quiz 1:  10% 
Quiz 2:  10% 
Midterm Exam:  25% 
Final Exam:  30% 
March 26:  Classes begin 
April 9:  Final day for electing use of the NonRecording Option (NRO) 
May 7:  Final day for dropping a fourth course without a grade notation of "W" 
May 15:  Final day to withdraw from a course 
May 28:  Memorial Day, no classes 
May 30:  Last day of classes 
June 2:  Math 60 final exam 
#  Date  Topics  Suggested HW & Announcements 


1  Mon, Mar 26  Class Information
What is probability? Intro to counting 
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2  Wed, Mar 28 
Quick review of writing proofs Homework 1 Assigned 
Suggested Homework: Start HW 1 Read handouts: Handout #1 Handout #2 Handout #3 

3  Fri, Mar 30  Combinations and permutations 
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4  Mon, Apr 2 
Proofs by Induction InclusionExclusion Laws of probability 
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5  Wed, Apr 4 
Conditional probability Homework 1 due Homework 2 assigned 
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6  Fri, Apr 6 
Bayes' Theorem Tree Diagrams Independence 
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7  Mon, Apr 9  Quiz 1 Review  
8  Tues, Apr 10 (Xhour) 
Quiz 1 (covers lectures 1—6)  
9  Wed, Apr 11 
Probabilistic paradoxes Homework 2 due Homework 3 delayed until Friday 

10  Fri, Apr 13 
Flavors of infinity Discrete vs. continuous Random variables Homework 3 assigned 
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11  Mon, Apr 16  Expected value 
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12  Wed, Apr 18  Variance and standard deviation 
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13  Fri, Apr 20 
Markov and Chebyshev's inequalities Homework 3 due Homework 4 assigned (due on Wednesday) 
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14  Mon, Apr 23  Discrete Distributions: Uniform, Bernoulli, Binomial 
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15  Tues, Apr 24 (Xhour) 
Exam 1 Review  
16  Wed, Apr 25 
Discrete distributions: Geometric, Negative Binomial
Homework 4 due Homework 5 assigned 
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17  Fri, Apr 27  Poisson Distribution 
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18  Mon, Apr 30 
Continuous distributions 
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19  Wed, May 2 
Uniform Distribution Exponential Distribution Homework 5 due Homework 6 assigned 
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20  Fri, May 4 
Gaussian (Normal) distribution Law of Large Numbers 
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21  Mon, May 7  Quiz 2 Review  
22  Tues, May 8 (Xhour) 
Quiz 2  
23  Wed, May 9 
Law of Large Numbers Homework 6 due Homework 7 assigned 
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24  Fri, May 11  Central Limit Theorem 
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25  Mon, May 14 
Central Limit Theorem Two Envelopes Paradox 
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26  Wed, May 16 
Two Envelopes Paradox Moment generating functions Homework 7 due Homework 8 assigned 
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27  Fri, May 18  Moment generating functions 
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28  Mon, May 21  Markov chains 
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29  Wed, May 23 
Absorbing Markov Chains (not finished yet) Homework 8 due Homework 9 assigned 
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30  Fri, May 25 
Absorbing MCs (finish) Ergodic and Regular MCs 
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Mon, May 28  Memorial Day—No Class  
31  Wed, May 30 
Random Walks Homework 9 due 
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Sat, June 2  Final exam 