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COMP_SCI 262: Mathematical Foundations of CS Part 2: Continuous mathematics for computer science


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Prerequisites

COMP_SCI 212 or equivalent (Math 300)

Description

The second part in the Mathematical Foundations of Computer Science (MFCS) sequence covers mathematical topics of probability, linear algebra, multivariable calculus and basic optimization that are crucial for many areas of modern computer science, including data science and machine learning. Unlike Part I of the MFCS sequence (CS212), this course will focus more on the above areas of continuous mathematics that are useful in computer science.

  • This CS 262 can count toward Statistic in CS Major Program (21 units).

List of Topics:
Probability: 

  1. Introduction to Probability: Random Events, Conditional Probabilities, Independence, Bayes Rule.
  2. Continuous probability distributions, Probability density function, CDF
  3. Normal distribution 
  4. Expectation, Linearity of Expectation, Variance of random variables.
  5. Markov's inequality. Chebychev inequality, Union bound.
  6. Sums of random variables, Central Limit Theorem, 
  7. Large deviation bounds, Statistical significance.
  8. Confidence bounds, precision, recall etc. 
  9. Monte Carlo methods and sampling

Linear Algebra

  1. Linear Algebra: High-dimensional vector spaces
  2. Eigenvalues, Eigenvectors.
  3. Principal Component Analysis and other application
  4. Connection to graph theory: Adjacency matrix, Edge-vertex matrix. Relating graph properties. 
  5. Random walks and Page Rank
  6. (Extra topic, if time) Linear Programming, LP Duality (2 lectures)

Calculus and Optimization

  1. Derivatives and Gradient.
  2. Gradient Descent
  3. Higher-order derivatives, convexity


COURSE INSTRUCTORS: Prof. Aravindan Vijayaraghavan

COURSE COORDINATOR: Prof. Aravindan Vijayaraghavan