Algebra : Theory of Equations, Matrices and Complex Numbers (mainly)

Algebra… The study of the one and only ‘x’, the ever unknown variable. Just kidding, algebra is much more than just all this. Although many books differ in what they classify algebra as, I am going to use algebra to basically cover the theory of equations, complex numbers, matrices, sequences and series, and a few minor chapters. Time’s of prime importance and so, let’s be on our way to discuss this essential unit of JEE-Mathematics syllabus. 

Chapter – Wise Analysis

  • Theory of Equations : Here, we shall be mainly dealing with quadratic equations and their applications. However, the same concepts can be used for higher order equations, such as cubic or biquadratic equations. Be prepared for questions on higher order polynomials! They are pretty common. Many neat tricks can be used in this chapter, like the Descartes Rule of Signs, especially for higher order polynomials. Don’t hesitate to solve questions graphically. Graphs help in visualization and boost speed and accuracy. Questions based on location of roots are easily solvable by graphical approach. Another important concept is how a quadratic equation represents a parabola and related properties. Practice a lot from this chapter to master it.
  • Principal of Mathematical Induction : An introduction to how mathematical proofs work. This chapter has no importance for JEE-Main or JEE-Advanced for the simple fact that questions based on this chapter are mainly subjective in nature. However, the method of induction should be known to all, atleast for their boards. No special preparation of this chapter needed for JEE.
  • Mathematical Reasoning : Another chapter with no importance in JEE-Advanced. However, a couple of sure shot questions are to be expected from this chapter in JEE-Main. The most important part of this chapter is Boolean logic. Practice it well. Keep in mind that there are a few parallels – ^ is like the AND gate, ~ is like NOT gate and so on.
  • Complex Numbers : The most important chapter of algebra, complex number holds a huge weightage in JEE. While easier questions are asked in JEE-Main, you’ll find hardly any direct questions of this chapter in JEE-Advanced. While the basic definitions and concepts are enough for JEE-Main, questions asked in JEE-Advanced require geometrical interpretation of complex numbers. Euler’s formula is of prime importance here. Practice a lot of questions of this chapter or you shall regret. 
  • Determinants & Matrices : I would not use this word for any chapter except this. It’s a boring one, especially the determinant part. Learn the basic properties of determinant manipulation and how to open determinants. That’s all for determinants. As far as matrices are concerned, properties of inverse, adjoint and transpose matrices are important. Also, there are a few named matrices like orthogonal, singular, unitary, etc. Make sure you know what each of these matrices are. 

Books for Algebra




All the Best,

Aakash Kapoor


30 thoughts on “Algebra : Theory of Equations, Matrices and Complex Numbers (mainly)”

  1. You told about A Das Gupta’s Problems in iit mathematics in your article ‘ Best books for jee’ . But now you are saying that SK GOYAL is good . Why don’t stick to one advice? I am getting confused every time.


    1. See, SK Goyal is good for the specific topic if you want additional practice in Algebra. A Das Gupta and McGraw Hill are the best balanced books there are. If you want complete practice, then go for these. For any specific topic, if you need additional practice, then only choose the books recommended in the topic-wise article.
      Hope this clarifies things.


  2. I started solving McGraw after solving my coaching material including previous year questions. Ironically I find Algebraic part more difficult than JEE. Solving each problem takes around 12 mins. Is it Okay?


  3. Hey aakash brilliant articles ,you tell all the imp topic and how to practice.Thanks,but the integral calculus page is not there .any guess what went wrong.


    1. Well, haven’t used cengage much and considering that the two are absolute classics level books, i would recommend the ones in the article


      1. Reading the full question is important 😛 Should have read the title 😛 😛


  4. I am using Higher Algebra — Hall and Knight and TMH for Algebra. Will this not be enough or SK GOYAL is must?


      1. He he you are right. I think I will take an all India test series from resonance and my coaching’s material will do. But still if I get time I will see other books.


      2. I have already brought that. I have seen that it has a variety and different type of questions and also there are many solved examples. But why are the first two chapters not included there. I mean , 1) Sets. 2) Relations and Functions. Rest all is fine. Another Q. A friend of mine said that TMH is only good for Algebra, rest of the questions are not that challenging. ??????


      3. Well, i found it good for all, especially calculus and coordinate. The tricks and comcepts that the book teaches u is more important than it being challenging as that varies from person to person


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