General Information

• Welcome to the class! 🙃
• The Course Website contains most materials. Please refer to Piazza for timely official announcements and logistical updates.
• This webpage contains supplementary notes and resources intended to complement my discussions at {MTWR 5-6p, TWRF 2-3p}.
• Note: I currently do not have officially scheduled office hours, but feel free to make an appointment with me via email (dbi@) if you would like to discuss something.
• Note: No lecture on Mon., Jun. 28 (and its corresponding discussions) due to the observation of Juneteenth.
• Note: No lecture on Mon., Jul. 5 (and its corresponding discussions) due to the observation of Independence Day.

Review Sessions

Session	Slides (full)	Slides (handout)
Final Review Session: PDFs and CDFs	Slides (full)	Slides (handout)
Midterm Review Session: Sets, Functions, and Cerdinality	Slides (full)	Slides (handout)

Discussion-Specific Content

• Week 1: Logic, Proofs, Sets, Cardinality

  Dis #	MTWR 5-6p	TWRF 2-3p	Remarks
  Dis 1A	5-6p Notes	2-3p Notes	{Partitions arising from propositions, duality in Boolean logic, and relation between Venn diagrams and Boolean logic} are not in scope.
  Dis 1B	5-6p Notes	2-3p Notes	{Orders of growth} are not in scope.
  Dis 1C	5-6p Notes	2-3p Notes	{The shift operator (<<)} is not in scope.
  Dis 1D	5-6p Notes	2-3p Notes	Optionally, try the problem on preserving set operations; it will help build your intuition on sets and functions. (Problem 2)

• Week 2: Cardinality, Computability (No Monday Lecture), Graphs, Modular Arithmetic

  Dis #	MTWR 5-6p	TWRF 2-3p	Remarks
  Dis 2A	5-6p Notes	2-3p Notes	Optionally, for motivation on graph theory, check out the talk "Networks of Oscillators That Synchronise Themselves," by Steven Strogatz.
  Dis 2B	5-6p Notes	2-3p Notes	e-GCD is quite important.
  Dis 2C	5-6p Notes	2-3p Notes	The formula for CRT, and intuition for its construction, are quite important.

• Week 3: (No Monday Lecture), Cryptography (RSA), Polynomials (Secret Sharing, Error Correcting Codes), Counting

  Dis #	MTWR 5-6p	TWRF 2-3p	Remarks
  Dis 3A	5-6p Notes	2-3p Notes	-
  Dis 3B	5-6p Notes	2-3p Notes	Homogeneous polynomials are not in scope.
  Dis 3C	5-6p Notes	2-3p Notes	Group theory (in particular, the discussion on the group S4) and metrics (in particular, the discussion on the manhattan distance metric on the grid) are not in scope.

• Week 4: Midterm; Counting, Probability, Conditionals, Bayes

  Dis #	MTWR 5-6p	TWRF 2-3p	Remarks
  Dis 4A	5-6p Notes	2-3p Notes	-
  Dis 4B	5-6p Notes	2-3p Notes	-
  Dis 4C	5-6p Notes	2-3p Notes	Be sure to understand the conditional probability formula and be comfortable applying it to simplify probabilities!

• Week 5: Independence, Random Variables, Variance, Covariance, Discrete Distributions

  Dis #	MTWR 5-6p	TWRF 2-3p	Remarks
  Dis 5A	5-6p Notes	2-3p Notes	A correction for a claim made in a previous discussion is contained in this discussion: PIE holds for all sample spaces (not necessarily uniform), while the ratio definition of probability holds for uniform sample spaces.
  Dis 5B	5-6p Notes	2-3p Notes	Linearity of expectation is a very useful concept!
  Dis 5C	5-6p Notes	2-3p Notes	-
  Dis 5D	5-6p Notes	2-3p Notes	-

• Week 6: Continuous Probability, Continuous Distributions, Joint Distributions

  Dis #	MTWR 5-6p	TWRF 2-3p	Remarks
  Dis 6A	5-6p Notes	2-3p Notes	-
  Dis 6B	5-6p Notes	2-3p Notes	-
  Dis 6C	5-6p Notes	2-3p Notes	-
  Dis 6D	5-6p Notes	2-3p Notes	-

• Week 7: Concentration Inequalities, Confidence Intervals, Markov Chains

  Dis #	MTWR 5-6p	TWRF 2-3p	Remarks
  Dis 7A	5-6p Notes, 5-6p Solutions	2-3p Notes	Due to low attendance, the 5-6p discussion was used to give a conceptual overview of concentration inequalities ("Notes"); my pre-written solutions to the worksheet are also provided ("Solutions").
  Dis 7B	5-6p Notes	2-3p Notes	-
  Dis 7C	5-6p Notes	2-3p Notes	-
  Dis 7D	5-6p Notes	2-3p Notes	-

• Week 8: Review; Final

  Good luck on the final!