
Explore algebraic manipulation by defining expressions, equations, identities, and inequalities, then learn to manipulate and solve problems using substitution, elimination, and creative approaches.
Master algebraic identities, from square and cube expansions to Sophie Gurman identity, and apply them to solve polynomial problems and prove key relations.
Explore sequences and series, including arithmetic, geometric, and harmonic progressions, and master sum formulas, problem-solving techniques, and arithmetic-geometric progression concepts for algebra.
Explore summation methods and properties, including cyclic sums and telescoping, to solve algebra problems. Learn the difference and telescoping strategies for APs and GPs, with practical examples.
Explore inequality methods in algebra, including sum of squares (Azores) and AM-GM inequalities, with practical problem-solving strategies to bound solutions, find maximums, and apply to equations.
Explore polynomials and theorems, learning about degree, coefficients, real and monic polynomials, and roots, then apply factor, remainder, and rational root theorems alongside Newton's Girard formulas to solve problems.
Explore quadratic expressions and equations, including factorization and completing the square (Hindu method). Analyze discriminants to determine real or imaginary, rational or integer roots, and understand common root scenarios.
If You have understood Basics of Mathematics then you should go for Algebra.
Why I prefer to Teach algebra first is because of its use in almost every branch of mathematics. Its not just about manipulating expressions, Algebra is a lot about how you use theorems to look at the given information in a different way and also to be able to create a mathematical relation defining the problem.
This Course include some very useful sections of Algebra (not permutations and Combinations, I will cover that in a separate course). These sections of Algebra are quite useful for competitive Exams. I have made sure that my approach is problem solving and not jargon.
There could be few lectures that you might need to watch more than once to grasp it completely. This course will build problem solving skills in you and will set you up to solve even Higher level exams like International Math Olympiads.
This course has video lectures, notes in pdf and workbooks to help you test your understanding along the way. To Navigate it better, Basics of Mathematics is organised into the following Sections
1) Algebraic Manipulations
2) Algebraic Identities
3) Sequences and Series
4) Advanced Summation Techniques
5) Inequality Method.
6) Polynomial and Theorems
7) Quadratic equations and Expressions
Each Subsection will have a set of video lectures followed by Assignments based on what is being taught in the section. Attempting
Assignment before moving to another section will be beneficial. Any doubts regarding the course can be asked in Q&A.
I hope you enjoy the course,
All the best