Hi, welcome to the blog once again. I guess you are just at the outset of your journey towards GATE. And I am sure you are well aware of your strengths and weaknesses by now. If not, I suggest you to go through Post #2.

So, let’s move on with more intense topic like “**WHAT TO STUDY**“. This is something that can not be discussed in a single post. Besides, I do not want this discussion to be contained within a single post only. I will discuss each and every module one by one. The discussions will contain name of reference study materials too.

“Strength doesn’t come from what you can do. It comes from overcoming the things you once thought you couldn’t.” −Rikki Rogers.

First of all, keep one thing in mind through out your preparation, GATE is a kind of exam which tests your basic understandings in a very smart way. It checks your ability to apply the knowledge you gathered. Cause in the end, Engineering is all about applications. Sometimes, you need to mold the solutions according to the situations. If you don’t know where and how to apply your knowledge, you simply don’t know anything about Engineering. Mindless cramming won’t take you anywhere. Whenever you are studying something, start questioning yourself. Grill yourself with questions like “What is this”, “How is this”, “Why is this”, “What if this was that” etc. This will seem like an exercise at the beginning, but more you do this, more it starts to become intrinsic to you. So, Let’s begin!

**† ***Before you begin, browse your 10+2 Mathematics book for the Algebra and Calculus part. It won’t take more than 1 or 2 days, but will help you a lot. Not required, if you are in touch with 10+2 Maths.*

Beyond doubt, Mathematics is the most important topic for CS students. Many of the CS subjects directly branch out from Maths itself and thus demand a good mathematical background. So I will begin my discussion with Maths. The following topics from Maths are in current syllabus –

- Linear Algebra
- Calculus
- Numerical Methods
- Set Theory & Abstract algebra
- Combinatories
- Probability Theory
- Mathematical Logic
- Graph Theory

Linear Algebra, Calculus and Numerical Methods are really nice and easy topics to begin with. Almost everyone has considerable amount knowledge in these parts. So, it will be easier to begin with these things before you start cracking some real hard nuts!

*•Linear Algebra:** [Questions are easy/moderate. May carry 1-3 marks]
*Matrix and Determinant, their properties and basic operations on them.

Special types of matrices like orthogonal,idempotent,diagonal,identity,symmetric,skew-symmetric,Hermitian,skew-Hermitian etc.

Transpose,Adjoint and Inverse of Matrix, how to calculate inverse by Gauss-Jordan method or by using characteristic equation.

Eigen values and Eigen vectors, properties of eigen values (e.g. ∑λ

_{i}=Trace of Matrix, ∏λ

_{i}=Det(A), If λ is an eigen value of A, then λ

^{m }is an eigen value of A

^{m }etc)

Characteristic equations, Cayley-Hamilton formula.

Rank of a Matrix.

Systems of linear homogeneous and non-homogeneous equations. Find number of solutions (unique,infinite or no solution) using rank.

*Ref. Book : Higher Engineering Mathematics by B.S. Grewal*

*(Erwin Kreyszig‘s book is the best in its class, it has much more challenging problems. But Grewal is enough for GATE.)*

*Further Ref: Introduction to Linear Algebra by Gilbert Strang*•*Calculus: [Questions are easy/moderate. May carry 2-3 marks]*

Functions, Limit(L’Hospitals rules included), Continuity, Differentiability, Mean Value Theorems (Geometrical interpretations too), Taylor series, Calculus of several variables, partial and total derivative, maxima and minima.

Integral calculus (all of 10+2), definite and improper integrals, properties, Beta, Gamma integrals.

*Ref. Book : Problems in Calculus of One Variable by I.A. Maron (Simply the best one!)*

For Calculus of several variables refer to B.S. Grewal.

For Calculus of several variables refer to B.S. Grewal.

*•Numerical Methods: [Questions are easy. May carry 1-2 marks]
*Bisection, Newton-Raphson, Secant method. Study their error estimation capabilities and order of convergences.

Trapezoidal and Simpson’s 1/3 rule. Their error estimation.

LU decomposition and solutions of systems of linear equations.

*Ref. Book : Introductory Methods in Numerical Analysis by S.S. Sastry (Although some online reference is more than sufficient in this area. Questions are straight forward.)*

If you have any further query regarding the above topics, then let me know. In the next post I will continue the discussion on other areas of Maths. Keep following!