Math Workshop for Political Science (Fall 2024)

The syllabus is available here.

Below is the schedule and the appropriate videos to watch before each session. These videos are meant to supplement textbook reading and spur class discussion. All of the videos are freely available from Khan Academy and YouTube (isn't it great that one's entire math education can be found for free online?!). I have included the most essential videos for each topic; however, going through additional ones, particularly for advanced topics, is suggested. Also, keep in mind that videos get taken down all the time for various reasons. If one is not available, please let me know, and do your best to find a replacement.

• Day 1: Intro, Notation and Definitions, and Some Basic Mathematics

  • Read this essay by Carol Dweck, "Even Geniuses Work Hard."

  • Read this short essay. Schwartz, Martin A. 2008. "The importance of stupidity in scientific research.'' The Journal of Cell Science 121: 1771. DOI:10.1242/jcs.033340.

  • Watch this video.

• Day 2: More Basic Mathematics

  • Summation operator

  • Product operator

  • Factorial

  • Permutations

  • Combinations

  • Solving equations of one variable

  • Solving equations of multiple variables

  • Inequalities

  • Quadratic formula

  • Solving for roots

  • Factoring

  • Logarithms

  • Log rules I

  • Log rules II

  • Exponents and rules

  • e and natural log

• Day 3: Linear Algebra I

  • Intro to Matrices

  • Linear equations and linear systems

  • Elementary matrix row operations

  • Adding and subtracting matrices

  • Multiplying matrices by scalars

  • Properties of matrix addition

  • Properties of matrix scalar multiplication

  • Matrix multiplication

  • Dot product I

  • Dot product II

  • Transpose

• Day 4: Linear Algebra II

  • Zero matrices

  • Identity matrix

  • Idempotent matrix

  • Linear dependence/independence

  • Linear combinations and span

  • Reduced row/row echelon form

  • Solving systems with RREF

• Day 5: Linear Algebra III

  • Matrix inversion

  • Conditions for non singularity (or, when can't you invert?)

  • Solving equations with inverses

  • Determinant

  • Trace

  • Matrix Rank

• Day 6: Linear Algebra IV and Calculus I (Introduction to Differentiation)

  • The difference quotient

  • Slope of a line secant to a curve

  • The derivative

  • The derivative from the difference quotient

  • The power rule

  • The chain rule (all videos on this link)

  • The product rule

  • The quotient rule

  • Derivative of exponential and log functions

• Day 7: Calculus II (More Differentiation) 

  • Partial differentiation

  • Intro to Limits

  • Limits and infinity

  • Differentiability and continuity

  • Higher Derivatives

• Day 8: Calculus III (Optimization and Constrained Optimization)

  • Definition of extreme values 

  • Relative minima and maxima

  • Concavity and second derivatives

  • Inflection points

  • Constrained optimization and Lagrange Multipliers

  • Polynomial approximation of a function I

  • Polynomial approximation of a function II

  • Taylor series approximation

• Day 9: Calculus IV (Integration)

  • Antidifferentiation

  • Areas and Riemann sums

  • Indefinite integrals 

  • Definite integrals

  • Fundamental Theorem of Calculus

• Day 10: Calculus V (More Integration)

  • Integration by substitution

  • Integration by parts

  • Improper integrals

  • Intro to calculus on matrices