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Course12710400360 lectures

Mathematical Tools for Cognitive Science

Prof. Himanshu Yadav · IIT Kanpur

Start with lecture 1 At NPTEL

About

This is a foundational course on Mathematics intended for students of Cognitive Science, Cognitive Systems, Psychology, and Linguistics. We are going to cover the following topics:. functions, differentiation, Matrix and Vector Algebra, Integration, multivariate calculus, and sets, probability, and random variables.

Intended audience: Cognitive Science students, Psychology students, Linguistics students, Biological and Neuroscience students

Lectures

Week 1

  1. Lecture 01: Real numbers and Exponents YouTube
  2. Lecture 02: Equations YouTube
  3. Lecture 03: Graphs YouTube
  4. Lecture 04: Graphs and Equations YouTube
  5. Lecture 05: Functions YouTube

Week 2

  1. Lecture 06: Inverse Functions YouTube
  2. Lecture 07: Graphs of Inverse Functions YouTube
  3. Lecture 08: Exponential Functions YouTube
  4. Lecture 09: Logarithmic Functions YouTube
  5. Lecture 10: Applications of Logarithmic and Exponential Functions YouTube

Week 3

  1. Lecture 11: Introduction to Trigonometric Functions YouTube
  2. Lecture 12: Sine and Cosine Functions YouTube
  3. Lecture 13: Trigonometric Identities YouTube
  4. Lecture 14: Trigonometric Identities: Examples YouTube
  5. Lecture 15: Representation of a point in a plane YouTube

Week 4

  1. Lecture 16: Introduction to Differentiation YouTube
  2. Lecture 17: Derivative of a Function YouTube
  3. Lecture 18: Some Basic Derivatives YouTube
  4. Lecture 19: Differentiation Examples YouTube
  5. Lecture 20: Practice Problems on Differentiation YouTube

Week 5

  1. Lecture 21: Maxima and Minima of a Function YouTube
  2. Lecture 22: Maxima and Minima examples YouTube
  3. Lecture 23: Partial Derivative YouTube
  4. Lecture 24: Least Squares Method YouTube
  5. Lecture 25: Differentiation Applications YouTube

Week 6

  1. Lecture 26: Introduction to Matrices YouTube
  2. Lecture 27: Matrix Operations YouTube
  3. Lecture 28: Inverse Matrix YouTube
  4. Lecture 29: Introduction to Vectors YouTube
  5. Lecture 30: Dot Product and Cross Product YouTube

Week 7

  1. Lecture 31: Introduction to Integration YouTube
  2. Lecture 32: Some Basic Integrals YouTube
  3. Lecture 33: Integration Examples YouTube
  4. Lecture 34: Substitution Method of Integration YouTube
  5. Lecture 35: Integration by Parts YouTube

Week 8

  1. Lecture 36: Introduction to Sets YouTube
  2. Lecture 37: Operations on Sets YouTube
  3. Lecture 38: Properties of Sets YouTube
  4. Lecture 39: Algebra of Sets YouTube
  5. Lecture 40: Sets and Probability YouTube

Week 9

  1. Lecture 41: Introduction to Probability YouTube
  2. Lecture 42: Probability Axioms YouTube
  3. Lecture 43: Probability Corollaries YouTube
  4. Lecture 44: Conditional Probability YouTube
  5. Lecture 45: Probability Examples YouTube

Week 10

  1. Lecture 46: Introduction to Random Variables YouTube
  2. Lecture 47: Discrete and Continuous Random Variables YouTube
  3. Lecture 48: Binomial and Poisson Distributions YouTube
  4. Lecture 49: Normal and Lognormal Distributions YouTube
  5. Lecture 50: Other Continuous Random Variables YouTube

Week 11

  1. Lecture 51: Probability Distributions in R YouTube
  2. Lecture 52: Continuous Random Variables in R YouTube
  3. Lecture 53: Random Variables Examples in R YouTube
  4. Lecture 54: Likelihood Function YouTube
  5. Lecture 55: Likelihood Function in R YouTube

Week 12

  1. Lecture 56: Joint Likelihood Function YouTube
  2. Lecture 57: Joint Likelihood in R YouTube
  3. Lecture 58: Parameter Estimation YouTube
  4. Lecture 59: Statistical Inference YouTube
  5. Lecture 60: Statistical Inference in the Bayesian Framework YouTube

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Kanpur
Department
Multidisciplinary
Teacher
Prof. Himanshu Yadav
Level
Undergraduate
Language
English
Subjects
Mathematics, Psychology and the brain
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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