Jay Pantone

John Wesley Young Research Instructor
Dartmouth College

jaypantone@dartmouth.edu


Math 20

Summer 2017

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. There is an honors version of this course: see MATH 60.

  • Lectures:
    M, W, F, 11:30am - 12:35pm
    Kemeny 105 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

Course Information

The official syllabus is here.

 
Homework Assignments

Announcements

Exams

Labs

Daily Calendar
# Date Topics Suggested HW
& Announcements
1 Fri, June 23 Class Information
What is probability?
Intro to counting
Suggested Homework:
R: # 1.1, 1.2, 1.4
2 Sat, June 24 Counting combinations Suggested Homework:
R: # 1.7,
GS: # 3.1.3, 3.1.6, 3.1.7, 3.1.10
3 Mon, June 26 Binomial Coefficients Suggested Homework:
GS: # 3.2.2, 3.2.10, 3.2.12
4 Tues, June 27
(X-hour)
Proofs and Proof Techniques Suggested Reading:
Handout #1
Handout #2
5 Wed, June 28 Events and Outcomes
Probability Laws
Announcements:
  • When suggested homework is assigned, that does not imply that you have to read the corresponding sections in the book. We will cover all the necessary material in class. If you have trouble with a problem, then you can read the book, but be aware that we are not covering every topic that the book does.
  • Homework 1 has been posted. See the link the in "Homework" section above.
Suggested Homework:
R: # 2.2, 2.3, 2.5, 2.8, 2.13
GS: # 1.2.2, 1.2.4
6 Fri, June 30 Probability Laws
Conditional Probability
Suggested Homework:
R: # 3.3, 3.4
GS: # 4.1.3, 4.1.22
7 Mon, July 3 Conditional Probability
Independence
Suggested Homework:
R: # 3.8, 3.9, 3.10
GS: # 4.1.4, 4.1.5a
8 Wed, July 5 Independence
Bayes' Theorem
Square Diagrams
Announcements:
  • Homework 1 due today.
  • Homework 2 assigned today.
Suggested Homework:
GS: # 4.1.16, 4.1.27, 4.1.29
9 Fri, July 7 Tree Diagrams
Probabilistic Paradoxes
Suggested Homework:
R: # 3.15
GS: # 4.1.30
10 Mon, July 10 Discrete Random Variables
Expectation
Suggested Homework:
GS: # 6.1.1, 6.1.2, 6.1.8, 6.1.16
11 Wed, July 12 Expectation
Variance
Announcements:
  • Homework 2 due today.
  • Homework 3 assigned today.
Suggested Homework:
GS: # 6.1.6, 6.2.4(a-d), 6.2.11, 6.2.14
12 Fri, July 14 Exam Review
Exam 1 (Look below for time and location.)
13 Mon, July 17 Variance and Standard Deviation Announcements:
  • We're using the X-hour tomorrow.
Suggested Homework:
GS: # 6.2.9, 6.2.23, 8.1.10
14 Tues, July 18
(X-hour)
The R Programming Language Announcements:
  • Lab 1 assigned today, due Wed, Aug 2.
Resources:
15 Wed, July 19 Markov's and Chebyshev's Inequalities
Infinite Discrete Spaces
Announcements:
  • Homework 3 due today.
  • Homework 4 assigned today.
Suggested Homework:
  • Same as July 17
16 Fri, July 21 Continuous Probability Spaces Suggested Homework:
GS: # 2.2.1, 2.2.2, 2.2.5, 2.2.6, 2.2.8
17 Mon, July 24 Distributions: Uniform, Bernoulli, Binomial Suggested Homework:
GS: # 5.1.1, 5.1.4, 5.1.9
18 Wed, July 26 Distributions: Geometric, Exponential Announcements:
  • Homework 4 due today.
  • Homework 5 assigned today.
Suggested Homework:
GS: # 5.2.29, 5.2.30, 5.2.34
19 Fri, July 28 Distributions: Poisson Suggested Homework:
R: # 5.3, 5.4, 5.7
GS: # 5.1.16. 5.1.18. 5.1.20. 5.1.22
Mon, July 31 Class canceled today.
20 Wed, Aug 2 Gaussian (Normal) Distributions
Simpson's Paradox
Announcements:
  • Lab 1 due today.
  • Homework 5 due today.
  • Homework 6 assigned today.
Suggested Homework:
GS: # 5.2.26, 5.2.28
21 Fri, Aug 4 Exam Review
Exam 2 (Look below for time and location.)
22 Mon, Aug 7 Adding Independent Random Variables Announcements:
  • Lab 2 assigned today.
Suggested Homework:
GS: # 7.1.2, 7.1.9, 7.2.2, 7.2.5
23 Wed, Aug 9 Weak Law of Large Numbers Announcements:
  • Homework 6 due today.
  • Homework 7 assigned today.
Suggested Homework:
GS: # 8.1.1, 8.1.4, 8.1.6, 8.1.11, 8.2.9, 8.2.11
24 Fri, Aug 11 Central Limit Theorem (GS, 9.1) Suggested Homework:
GS: # 9.1.1, 9.1.2, 9.1.4, 9.1.5, 9.1.6, 9.1.9 ,9.1.13
25 Mon, Aug 14 Central Limit Theorem (GS, 9.2) Suggested Homework:
GS: # 9.2.1, 9.2.3, 9.2.5, 9.2.6, 9.2.7
26 Tues, Aug 15
(X-hour)
Two Envelopes Paradox
Benford's Law
Suggested Homework:
GS: 4.3.4, 4.3.5, 5.1.45 (in R, using this function)
27 Wed, Aug 16 Central Limit Theorem (GS, 9.3)
Markov Chains (GS, 11.1)
Announcements:
  • Homework 7 due today.
  • Homework 8 assigned today.
Suggested Homework:
GS: # 9.3.11, 9.3.13, 11.1.2., 11.1.4, 11.1.7, 11.1.11
28 Fri, Aug 18 Markov Chains (GS, 11.2)
(didn't finish)
Suggested Homework:
   will be given on Monday
29 Mon, Aug 21 Markov Chains (GS, 11.2) Announcements:
  • Lab 1 due today.
Suggested Homework:
GS: # 11.2.2, 11.2.6, 11.2.8, 11.2.12, 11.2.19
30 Wed, Aug 23 Markov Chains (GS, 11.3) Announcements:
  • Homework 8 due today.
  • Office Hours before the exam:
    • Thursday, 1pm - 3pm
    • Friday, 12pm - 2pm
Suggested Homework:
GS: # 11.3.1. 11.3.2. 11.3.3. 11.3.5. 11.3.12
Sun, Aug 27 Final exam (Look below for time and location.)

Syllabus

The official syllabus is here.

 
Homework Assignments

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

Exam Dates
Exam 1: Friday, July 14, 5:00pm - 7:00pm — Kemeny 006
Exam 2: Friday, August 4, 5:00pm - 7:00pm — Kemeny 006
Final Exam: Sunday, August 27, 8:00am - 11:00am — Kemeny 105

Textbooks
Grading Scheme
Homework: 25%
Labs: 10%
Exam 1: 20%
Exam 2: 20%
Final Exam: 25%

Important Dates
June 22: Classes begin
June 24: Special Saturday day of classes
July 4: Independence Day, no classes
July 6: Final day for electing use of the Non-Recording Option (NRO)
August 2: Final day for dropping a fourth course without a grade notation of "W"
August 9: Final day to withdraw from a course
August 23: Last day of classes
August 27: Math 20 final exam