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Supriya Singhal

The course intends to cover basics of few chapters of Mathematics optionals specifically the ones like modern Algebra. Aspirants appearing cse mains with maths  as their optionals will find it really useful.

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Modern Algebra: Group Theory - Mathematics Optionals for UPSC CSE

Crash Course

Basic Numeracy 

CSAT - Paper II

UPSC CSE

Ace the toughest competitive and government exams in India 

Test Preparation

Union Public Service Commission Exams (UPSC)

Basic Numeracy

UPSC - Numeracy - Crash Course

This is the overview of the course. This lesson presents the importance of Modern Algebra and  lays the expectation for the lessons to follow!

Overview of the Course

This is the first lesson covering the very basics of group theory. It explains the definition of a group and it's properties.

Modern Algebra: Part 1

This is the second lesson on group theory. It defines groups on finite sets through the concept of Cayley table.

Modern Algebra: Part 2

This is lesson 3 of group theory. It describes two new operations- addition modulus n and multiplication modulus n and constructs Cayley tables using that.

Modern Algebra: Part 3

This is lesson 4 of group theory. Here we take different ( weird ) operations and operate them on sets to see if they form a group.

Modern Algebra: Part 4

This is the 5th lesson on group theory. It continues from the last lesson and takes examples of different sets and operations and checks whether sets form a group or not!

Modern Algebra: Part 5

This is part 6 of the group theory. Here we have taken matrices as the set and operation as multiplication and addition.

Modern Algebra - Part 6

This is part 7 in group theory. Here we learn two cases of matrices GL and SL.

Modern Algebra -Part 7

This is part 9 in the group theory. Here we take a peculiar case of set of translation function wrt composite as operation. We also prove 2 universal properties of a group.

Modern Algebra -Part 8

This video explains the third property of a group - cancellation laws. Also, explains what is the inverse of an element in a group

Modern Algebra -Part 9

This lesson continues with the properties of a group. Inverse, multiplication and solvability is discussed.

Modern Algebra -Part 10

In this lesson we discuss what is a semigroup. Then we proof how a semigroup can become a group.

Modern Algebra -Part 11

In this lesson we take few questions and solve them. Answer writing format is shown which can be helpful while attempting mains.

Modern Algebra- Part 12

This lesson takes another set of questions on group.

Modern Algebra -Part 13

The lesson continues with questions but here we have introduced the method of mathematical induction to solve questions.

Modern Algebra-Part 14

This lesson takes an interesting question where there are three parts to a  question and mathematical induction is just one part of the solution.

Modern Algebra -Part 15

This lesson takes 2 interesting and different questions- one on matrices and other on odd and even no of elements in a group.

Modern Algebra -Part 16

This lesson continues on the path of solving interesting questions on group theory.

Modern Algebra -Part 17

Here we take the U (n) example which is one of its kind. Also, some rapid fire questions to make the course interesting.

Modern Algebra -Part 18

Here we revise the previous portion and also solve some rapid fire questions. Then we continue to solve question on prime no.

Modern Algebra -Part 19

This is a video which takes revision of matrices and groups.

Modern Algebra -Part 20

In this lesson we take a statement that - group with 4 or less elements is Abelian and try to proove it.

Modern Algebra - Part 21

We continue with the statement of previous video and prove it for a group with 3 and 4 elements.

Modern Algebra -Part 22

This lesson takes the question on matrices and shows how to write the solution...

Modern Algebra -Part 23

This is a revision cum new questions video on groups

Modern Algebra -Part 24

This is the last part in question series on group.

Modern Algebra -Part 25

This is the new topic in group theory- Subgroups

Modern Algebra - Part 26

This lesson is 2nd in the topic of subgroups.

Modern Algebra - Part 27

Third lesson in subgroups with 3 examples of how to prove a set is subgroup.

Modern Algebra- Part 28

This is the 4th lesson in the subgroup discussing finite subgroup test and it's proof

Modern Algebra -Part 29

This lesson covers few examples of using subgroup tests. Also, we start with few special subgroups - centre of a group

Modern Algebra -Part 30

Thus lesson continues with the special subgroups. We find centralizer of an element, centralizer of the subgroup, normaliser of a subgroup and conjugate of a subgroup and prove all these are themselves also a subgroup.

Modern Algebra -Part 31

Can Modern Algebra help you in other topics?

Huge thank you for the love so for and what lies ahead in this course!

Notice

This is regarding new course on solving previous year questions of maths. LPP is the first topic that is being covered.

A new course

Cyclic groups

Order of a group

This takes three theorems 
1. Order of an element and it's inverse is same 
2. Order of element is same as it's conjugate 
3. Order of ab= order of ba

This lesson explains the concept of cyclic group - the basics

Order of group

Thus lesson explains the theorem - generator having infinite order generates group of infinite order

Cyclic group -1

Cyclic group and order

Most important theorem of cyclic group - the subgroup of a cyclic group is also cyclic

More underatanding on theorem and division algorithm

This lesson explains the generators and their order

Cyclic order

Continued...

Important question on how to derive a cyclic group

Examples and questions

Examples and questions continued

Homomorphism and isomorphism

Homomorphism - Part 2

First v theorem- homomorphic image of a subgroup is a subgroup

Homomorphism - preservation theorems

Homomorphism - , preservation theorem 2

Permutation group - part 1

Permutation group -2

Permutation group -3

Permutarion group-4

MASTERS from Dr R.M.L Awadh Uni.Ayodhya and BACHELOR of EDUCATION from MGKVP Varanasi .Teaching experience up to 8 yrs. EXPERT in CTET/TETs.

Alok Prakash Jha

In this course, the educator discusses Previous year questions of Maths. The course will be beneficial for UPSC CSE aspirants.

(Hindi) Maths for UPSC CSE

I have 10 years teaching experience in maths related to all competitive exam and I have uploaded a lot of videos in my youtube channel

Shivcharan Singh Negi

This course deals with all the concepts and questions in the very important chapter Binomial Theorem on probablity

(Hindi) UPSC: The Binomial Theorem on Probability

Arpita Sharma

This course has been developed by Arpita Sharma for beginners to make them equipped with basic formulas they lack for solving various questions in CSAT paper of UPSC,quant sections of bank exams as well. 
various previous years questions are solved in this course based on these formulas.

Daily Course on Quantitative Aptitude for UPSC CSE

B.Tech. (ECE '15), IIT Kharagpur,
AIR 34 in AIEEE - 2011,
Qualified RMO - 2009,
CSE Mains 2017: Essay - 153, Maths - 252

Asim Anand

This course is a continuation of the course "Mathematics Optional for UPSC - Dynamics".

Mathematics Optional for UPSC - Dynamics II

I have four years of experience of teaching  maths. 

Neha Sharma

In this course, the educator discusses Number System and Series for UPSC CSAT Paper 2

(Hindi) Number System and Series: UPSC CSAT Paper 2

Have qualified SSC CGL, HSSC PGT & TGT, SLET/NET, CTET, KVS,SBI P. O. WRITTEN EXAMS. Top Unacademy educator 2017.

Dr Anshu Sheoran

How to solve HCF and LCM related problems with tricks and how to solve word problems using them.

Lessons

55 lessons • 12h 3m

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Overview of the Course

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Modern Algebra: Part 1

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Modern Algebra: Part 2

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Modern Algebra: Part 3

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Modern Algebra: Part 4

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Modern Algebra: Part 5

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Modern Algebra - Part 6

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Modern Algebra -Part 7

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Modern Algebra -Part 8

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Modern Algebra -Part 9

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