
Linear Algebra




Lecture 1A  Why Study Linear Algebra
22:00




Lecture 1B  Linear Algebra for GATE & Interviews
14:00




Annotated Notes  Lecture 1A1B
(32 pages)




Lecture 1C  Linearly Independent and Linearly Dependent
75:00




Annotated Notes  Lecture 1C
(92 pages)




Lecture 2A  Filling the Space Part 1
44:00




Lecture 2B  Filling the Space Part 2
28:00




Lecture 2C  Summary So far
12:00




Lecture 2D  Multiplying a Matrix & a Vector
26:00




Annotated Notes  Lecture 2
(103 pages)




Homework 1  Linear Dependence & Independence
(12 pages)




Live Session 1  Homework 1 Discussion




Annotated Notes  Live Session 1
(20 pages)




Lecture 3A  Why Solve System Of Linear Equations
22:00




Lecture 3B  Writing as Ax=b, Geometric Interpretation and Possible Solutions
24:00




Lecture 3C  Understanding Ax=b intuitively
44:00




Lecture 3 Annotated Notes
(74 pages)




4a. Multiplying 2 Matrices  My Walmart Interview Question
18:00




4b. GATE 2016 Question
16:00




4c. GATE 2014 Question
14:00




4d. Two conceptual questions
28:00




4e. Linear Combination of Independent vectors is unique
28:00




4f. GATE 2017 Question
4:00




Lecture 4 Annotated Notes
(76 pages)




(New) Practice Questions based on Concepts covered upto lecture 4F
80:00




Annotated Notes Practice Questions based on Concepts covered upto lecture 4F
(79 pages)




(New) Practice Questions based on Concepts covered upto lecture 4F  Part2
82:00




Annotated Notes Practice Questions based on Concepts covered upto lecture 4F Part2
(82 pages)




Weekly Quiz 3  Fundamental Course and Linear Algebra
(7 pages)




(New) Weekly Quiz 3 GATE 2025 Solution
100:00




Annotated Notes Weekly Quiz 3 Linear Algebra
(64 pages)




Homework 2
(20 pages)




5a. Echelon Form and Pivot Columns
37:00




5b. Gaussian Elimination
26:00




Live Session 2




Live Session 2 Annotated Notes
(48 pages)




5c. Rank  GATE 1994 Question  Rank Nullity Theorem
11:00




5d. Finally Solving Ax=b  Five Different Questions
33:00




5e. More than one free variable in 𝐴𝑥=0 solution
32:00




Lecture 5 Annotated Notes
(125 pages)




Live Session 3




Live Session 3 Annotated Notes
(18 pages)




6a. GATE 2021 Question  Free variables in Non homogeneous
19:00




6b. Solutions based on Rank(A) and Rank(Ab)
18:00




6c. Few Questions related to rank(A) and Number of solutions
8:00




6d. [OPTIONAL] Linearly Independent Columns with Gaussian Elimination
24:00




6e. [Optional] Row Reduced Echelon Form
28:00




Lecture 6 Annotated Notes
(74 pages)




Homework Questions Set 2
(20 pages)




Lecture 7 Determinant
100:00




Lecture 7b Inverse of a Matrix




Lecture 7c. Crammer's rule
26:00




Lecture 7 Annotated Notes
(149 pages)




Live Session 4




Live Session 4 Annotated Notes
(42 pages)




Lecture 8a. Introduction to Eigenvalues and Eigenvectors
23:00




Lecture 8b. Characterstic Equation
15:00




Lecture 8c. Solving for Eigenvalues and Eigenvectors
22:00




Lecture 8 Annotated Notes
(45 pages)




Lecture 9a. Linearly Independent eigen vectors with repeating eigenvalues
21:00




Lecture 9b. Three Different Examples With Repeating Lambda
30:00




Lecture 9c. Symmetric Matrices has n LI Eigen Vectors
12:00




Lecture 9d. Two Magical Properties
12:00




Lecture 9 Annotated Notes
(95 pages)




Live Session 5




Live Session 5 Annotated Notes
(131 pages)




10a. Rank and Eigen Values
22:00




10b. Examples on Rank and Eigen Values
15:00




10c. CAYLEYHAMILTON THEOREM
16:00




10d. Eigen Values of AB and BA
32:00




10e. Eigen Values of Powers of A
17:00




Lecture 10 Annotated Notes
(99 pages)




Live Session 6 (Three Tough/Interesting GATE PYQs)




Live Session 6 Annotated Notes
(14 pages)




Weekly Quiz 6  Linear Algebra
(10 pages)




Lecture 11a. LU Decomposition
25:00




Lecture 11b. Type Of Matrices
84:00




Lecture 11 Annotated Notes
(80 pages)




Weekly Quiz 7  Linear Algebra
(9 pages)




Live Session 7 Weekly Quiz Solutions




Live Session 7 Annotated Notes
(59 pages)




Live Session 8 Weekly Quiz 7 LA Solutions




Live Session 8 Annotated Notes
(23 pages)




Annotated Notes Scholarship test Linear Algebra Solution
(63 pages)



Probability




Lecture 1a Probability Definition, Sample Space and Events
28:00




Lecture 1b. Inclusion Exclusion Principle, Demorgan's Law
37:00




Lecture 1 Annotated Notes
(40 pages)




Lecture 2a. Conditional Probability Introduction
34:00




Lecture 2b. Conditional Probability Examples
26:00




Lecture 2c. Introduction to Tree Diagram
32:00




Lecture 2 Annotated Notes
(70 pages)




Lecture 3a. Total Probability
36:00




LIVE Session 1: GATE PYQs Tree Method




Live Session 1 Annotated Notes
(35 pages)




Lecture3b. Conditional Probability Examples
33:00




Lecture 3 Annotated Notes
(55 pages)




Lecture3c. GATE PYQs and Bayes Theorem




Annotated Notes Lecture3c. GATE PYQs and Bayes Theorem
(48 pages)




[Optional] My LinkedIn Interview
49:00




[Optional] My Linkedin Interview
(28 pages)




Lecture 4a. Indepence of events
43:00




Lecture 4b. Conditional Independence
32:00




Lecture 4 a,b Annotated Notes
(61 pages)




Lecture 4c. Independence Does not imply Conditional Independence
22:00




Lecture 4c Annotated Notes
(22 pages)




Lecture 4d: Random Variables Introduction




Annotated Notes Lecture 4d: Random Variables Introduction
(46 pages)




Lecture 5a. Practice Questions on Random Variables
29:00




Lecture 5a. Indepence of events
(20 pages)




LIVE Session 4: Practice Questions on Random Variables




Live Session 4 Annotated Notes
(46 pages)




Weekly Quiz 8  Conditional Probability
(6 pages)




LIVE Session 5: Weekly Quiz 8 (Conditional Prob) Discussion




Live Session 5 Annotated Notes
(56 pages)




Lecture 6a. Types of Random Variables
9:00




Lecture 6b.Probablity Mass Function Questions Part 1
20:00




Lecture 6c.Probablity Mass Function Questions Part 2
15:00




Lecture 6 Annotated Notes
(39 pages)




Lecture 7a. Expectation of Discrete Random Variable
19:00




Lecture 7b Expectation vs Average
40:00




Lecture 7c.[Optional] Expectation as center of mass
8:00




Lecture 7d. MIT Question and GATE 2021 Question
13:00




Lecture 7e. Expectation of Random Variable which is a Function of Random Variable
18:00




Lecture 7 Annotated Notes
(70 pages)




LIVE Session 6




Live Session 6 Annotated Notes
(35 pages)




Lecture 8a. Question number 8
21:00




Lecture 8b. Question number 9, 10, 11
17:00




Lecture 8c. Question number 12, 13
30:00




Lecture 8 Annotated Notes
(37 pages)




Lecture 9a. Cumulative Distribution Function
31:00




[LIVE] Lecture 9b  Variance Intuition and Formula
52:00




[LIVE] Lecture 9c Variance Main Formula and Questions
38:00




[LIVE] Lecture 9d Variance Questions
45:00




Lecture 9 Annotated Notes
(85 pages)




[LIVE] Lecture 10a: Discrete random variable (Bernoulli and Binomial RVs)
77:00




[LIVE] Lecture 10b. MIT Question on Binomial RV
16:00




[LIVE] Lecture 10c. Optional and Skip  Question on Plot of PMF
19:00




[LIVE] Lecture 10d. Poisson RV
28:00




10d. Discrete Uniform RV Introduction
15:00




[LIVE] Lecture 10 Annotated Notes
(79 pages)




Lecture 11a. Introduction to Continuous Distributions  Intuition about PDF
32:00




Lecture 11b. Continuous Uniform Distribution
25:00




Lecture 11c. Normal Distribution
43:00




Lecture 11d. Normal Distribution  2
17:00




Lecture 11e. Exponential Distribution
18:00




Lecture 11 Annotated Notes
(83 pages)




Lecture 12. Statistics  Mean Mode Median
35:00




Lecture 12 Annotated Notes
(20 pages)




LIVE: Weekly Quiz 11 Discussion : Random Variables and Probability Distributions




Annotated Notes  Weekly Quiz 11 Discussion  Random Variables & Probability Distributions
(47 pages)




Weekly Quiz 11  Probability Distributions
(7 pages)



Calculus




Calculus Lectures Complete Playlist




Limits in Calculus  Calculus  Engineering Mathematics  GATE  GO Classes  GATE Overflow
50:00




Continuity in Calculus  Calculus  Engineering Mathematics  GATE  GO Classes  GATE Overflow
12:00




Differentiability in Calculus  Calculus  Engineering Mathematics  GATE  GO Classes
17:00




Maxima Minima in Calculus  Calculus  Engineering Mathematics  GATE  GO Classes
28:00




Intermediate Value Theorem  Calculus  Engineering Mathematics  GATE Computer Science
18:00




Rolle's Theorem and Examples  Calculus  Engineering Mathematics  GATE Computer Science
13:00




Integration with ALL GATE PYQs  Tic Tac Toe method  Engineering Mathematics  GO Classes
44:00




Limits Annotated Notes
(24 pages)




Continuity Annotated Notes
(8 pages)




Differentiability Annotated Notes
(7 pages)




Maxima and Minima Annotated Notes
(15 pages)




Integration Annotated Notes
(31 pages)




Intermediate Value Theorems Annotated Notes
(15 pages)




LIVE Session 1: Limit and Continuity




LIVE Session 1 Annotated Notes
(86 pages)




LIVE Session 2: Differentiability




LIVE Session 2 Annotated Notes
(107 pages)




LIVE Session 3: Double Derivative and Mean Value Theorems




LIVE Session 3 Annotated Notes
(83 pages)




LIVE Session 4: Integration




LIVE Session 4 Annotated Notes
(74 pages)




Calculus Quiz  Weekly Quiz 14




Weekly Quiz 14  Calculus
(10 pages)




Annotated Notes  Calculus Quiz Discussion
(70 pages)



Students' Hand Written Notes




Engineering Mathematics Notes  by Quantum City
(36 pages)




Linear Algebra Notes  by Aditya
(121 pages)




Probability Notes  by Aditya
(141 pages)

