Jay Pantone

Assistant Professor
Marquette University

jay.pantone@marquette.edu


Math 60

Spring 2018, Dartmouth College

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 (X-hour)
  • 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

Course Information

The official syllabus is here.

 
Homework Assignments

Weekly graded homework assignments, posted above. Daily suggested homework from the textbook, not graded.

Announcements

Exams

Quiz and Exam Dates
Quiz 1: Tuesday, April 10
Exam 1: Tuesday, April 24
Quiz 2: Tuesday, May 8
Final Exam: Saturday, June 2

Textbooks
Grading Scheme
Homework: 25%
Quiz 1: 10%
Quiz 2: 10%
Midterm Exam: 25%
Final Exam: 30%


Important Dates
March 26: Classes begin
April 9: Final day for electing use of the Non-Recording 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

Daily Calendar
# Date Topics Suggested HW
& Announcements
1 Mon, Mar 26 Class Information
What is probability?
Intro to counting
Suggested Homework:
P: # 1.1.3, 1.1.5, 1.1.6
GS: # 3.1.3, 3.1.6, 3.1.10, 3.1.12
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 Suggested Homework:
P: # 2.1.1, 2.1.2, 2.1.7
GS: # 3.1.14, 3.1.15, 3.2.12, 3.2.19, 3.2.21, 3.2.24, 3.2.25
4 Mon, Apr 2 Proofs by Induction
Inclusion-Exclusion
Laws of probability
Suggested Homework:
P: # 1.3.13, 1.3.14, 1.3.15
GS: # 1.2.6, 1.2.7
5 Wed, Apr 4 Conditional probability
Homework 1 due
Homework 2 assigned
Suggested Homework:
P: # 1.4.3, 1.4.5(c), 1.4.6, 1.4.9, 1.4.12
GS: # 4.1.1, 4.1.3, 4.1.4, 4.1.6
6 Fri, Apr 6 Bayes' Theorem
Tree Diagrams
Independence
Suggested Homework:
P: # 1.5.1, 1.5.2, 1.6.3, 1.6.4, 1.6.7
GS: # 4.1.14, 4.1.18, 4.1.19, 4.1.25
7 Mon, Apr 9 Quiz 1 Review
8 Tues, Apr 10
(X-hour)
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
Suggested Homework:
P: # 3.1.1, 3.1.3, 3.1.13a
11 Mon, Apr 16 Expected value Suggested Homework:
P: # 3.2.3, 3.2.4, 3.2.5, 3.2.13
GS: # 6.1.1, 6.1.2, 6.1.8, 6.1.16
12 Wed, Apr 18 Variance and standard deviation Suggested Homework:
P: # 3.3.2, 3.3.3, 3.3.4
GS: # 6.2.4(a-d), 6.2.9, 6.2.11, 6.2.14, 6.2.23
13 Fri, Apr 20 Markov and Chebyshev's inequalities
Homework 3 due
Homework 4 assigned (due on Wednesday)
Suggested Homework:
P: # 3.2.8, 3.2.11, 3.3.12(a), 3.3.13(a-b), 3.3.15, 3.review.13
GS: # 6.2.12, 8.1.10
14 Mon, Apr 23 Discrete Distributions: Uniform, Bernoulli, Binomial Suggested Homework:
P: # 2.1.{4,5,6,8,10,13}
GS: # 5.1.{1,2,6}
15 Tues, Apr 24
(X-hour)
Exam 1 Review
16 Wed, Apr 25 Discrete distributions: Geometric, Negative Binomial Homework 4 due
Homework 5 assigned
Suggested Homework:
P: # 3.4.{1,3,7,9,14,19}
GS: # 5.1.{8,25}
17 Fri, Apr 27 Poisson Distribution Suggested Homework:
P: # 3.5.{1,2,4,5,6,9,10}
GS: # 5.1.{14,21}
18 Mon, Apr 30 Continuous distributions
Suggested Homework:
P: # 4.1.{2,3,5}
GS: # 2.2.{1,2,4,5,6,8abd}
19 Wed, May 2 Uniform Distribution
Exponential Distribution
Homework 5 due
Homework 6 assigned
Suggested Homework:
P: # 4.2.{3,8}
GS: # 5.2.{1,2,9,29,31}
20 Fri, May 4 Gaussian (Normal) distribution
Law of Large Numbers
Suggested Homework:
GS: # 5.2.{25,26,27,28}
21 Mon, May 7 Quiz 2 Review
22 Tues, May 8
(X-hour)
Quiz 2
23 Wed, May 9 Law of Large Numbers
Homework 6 due
Homework 7 assigned
Suggested Homework:
GS: # 8.1.{1,4,6,8,11}, 8.2.{9,11}
24 Fri, May 11 Central Limit Theorem Suggested Homework:
GS: # 9.1.{1,2,4,5,9,13}
25 Mon, May 14 Central Limit Theorem
Two Envelopes Paradox
Suggested Homework:
GS: # 9.2.{1,3,5,6,7}, 9.3.{11,13}
26 Wed, May 16 Two Envelopes Paradox
Moment generating functions
Homework 7 due
Homework 8 assigned
Suggested Homework:
GS: # 4.3.{4,5}, # 10.1.{none yet}
27 Fri, May 18 Moment generating functions Suggested Homework:
GS: # 10.1.{1 (just \(g(t)\)),7,11}, 10.3.{1,3ab,7}
28 Mon, May 21 Markov chains Suggested Homework:
GS: Read examples 11.4-11.12 in section 11.1
# 11.1.{2,4,7,11,17,18}
29 Wed, May 23 Absorbing Markov Chains
(not finished yet)
Homework 8 due
Homework 9 assigned
Suggested Homework:
GS: # 11.2.{3,6,7,9,13,15}
30 Fri, May 25 Absorbing MCs (finish)
Ergodic and Regular MCs
Suggested Homework:
GS: # 11.3.{1,2,3,5,8,10,11,12,17}
Mon, May 28 Memorial Day—No Class
31 Wed, May 30 Random Walks
Homework 9 due
Suggested Homework:
GS: # 12.1.15
Sat, June 2 Final exam