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Supriya Singhal

The course covers a very vast and difficult topic of Modern Algebra called Rings. Although many aspirants with mathematics optionals find this topic heatwreckening we will break this myth by simplifying the topic. It's recommended that viewers try watching the Modern Algebra part 1 course made by me. If due to lack of time or any other reason it's not possible then please watch part 1 to 10 and then part 22 to 25.
Here is the link 
https://unacademy.com/course/mathematics-optionals-for-upsc-cse/V8RIOPTU

Crack UPSC CSE Prelims and Mains Exams. Know how to prepare for UPSC 2019 and 2020, complete syllabus, exam patterns, latest notifications to join IAS, IFS, IPS and other cadres of Civil Services.

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UPSC - Civil Services Examination (IAS) Preparation

Hindi

(Hindi) Part 1: Rings And Subrings - Mathematics Optionals For UPSC CSE

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Union Public Service Commission Exams (UPSC)

Syllabus

This is the overview of the rings and subrings course. Rings form a very important part of modern Algebra and can be scoring if learnt the right way!

Rings and Subrings - Overview

This is the introductory lesson for rings!! It explains how rings are different from groups.

Rings- Part 1

This lesson explains the 9 properties needed for a set to become ring and how can you extend groups and concepts of group to rings!

Rings - Part 2

This lesson starts with properties of rings. First property of cancellation laws hold in ring with respect to addition is proved. Second property of any element multiplied by zero gives zero in a ring is also started.

Rings- Part 3

This lesson takes the properties of rings and shows how to prove them.

Ring - Part 4 (in Hindi)

This lesson discusses the 4th property of rings  which is distributive laws wrt to subtraction. Then we differentiate between unit and unity element and start with the most important topic of rings- classification of rings( type of rings).
We learnt about right with unity, commutative ring and CRU.

Ring - Part 5 (in Hindi)

This lesson continues with classification of rings. We cover DR, CRU, integral domain and a field.

Rings - Part 6 (in Hindi)

This lesson starts with the examples of how to prove a set to be a ring.

Rings - Part 7 (in Hindi)

In this video we discussed three type of questions
1. Example of infinite fields
2. Example of infinite ID which is not a field 
3. Example of finite field

Rings Part- 8 (in Hindi)

In this lesson we discussed examples of finite ring which is field and ID, a finite ring which is a CRU but neither a field nor an ID. Also, we discussed a ring which is RU but not a field and not an ID

Ring - Part 9 (in Hindi)

In this lesson cancellation laws wrt multiplication in a ring are discussed. Also, two theorems- every field is an ID but vice versa not true are proved.

RINGS - PART 10 (in Hindi)

This lesson continues with examples but of very different kinds.

Rings - Part 11 (in Hindi)

This lesson takes another set of examples with operations based on Addison and multiplication but not the simple ones!

Rings - Part 12 (in Hindi)

This lesson takes a peculiar question where in a set can be proved to be a ring only with the help of another set.

Rings - Part 13 (in Hindi)

In this lesson we proof the theorem that the ring has no zero divisors iff cancellation laws hold.

Rings - Part 14 (in Hindi)

Theorem- a commutative ring with unity is an ID when cancellation laws hold in the ring

Rings - Part 15 (in Hindi)

Rings- Part 16 (in Hindi)

A finite commutative ring with no 0 divisors is a field. (Theorem using pigeon hole principle)

Rings- Part 17 (in Hindi)

This video explains how to find multiplicative inverse of elements in Zp ring an hence proves it to be a ring.

Rings - Part 18 (in Hindi)

Learnt how to decide which operation to put to make a set ring

Rings- Part 19 (in Hindi)

Previous year questions on boolean ring is solved and the concepts of idempotenband nil potential element are also discussed.

Rings - Part 20 (in Hindi)

Theorems for when will the closure wrt addition and multiplication become nilpotent and why does this not happen for a  non commutative ring.

RINGS - PART 21 (in Hindi)

Rings - Part 22 (in Hindi)

This is the last lesson of the topic of basic of rings. Examples and pe new concepts with an amazing closure to video!

Rings - Part 23 (in Hindi)

Rings - Part 24

Rings - Part 25

Rings - Part 26

Rings - Part 27

Rings - Part 28

 specialize in Advance current affairs , Newspaper  analysis , Science and Tech and Agriculture optional + 10 yrs teaching experience .

Saurabh Pandey

In this course the attempt is made to improve the answer writing skill. On regular basis the lessons will be published . Each lessons will have different themes taken from different subjects based on which the questions will be asked.

(Hindi) UPSC/IAS Mains Answer Writing for IAS Mains 2019 and 2020.

Founder - Anuj Garg Coaching I 9 years of teaching experience | Use my code "AGC10"  to Unlock free content | 

Anuj Garg

In this course I will be dealing with some important previous year questions asked in history optional

(Hindi) Target History Optional-2019/20

In this course I will be discussing some important questions asked in UPSC mains from modern history section

(Hindi) Modern History Previous Year Paper Analysis (2014-2018)

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4+ Years of Teaching experience for IIT JAM, CSIR NET
Provided Top Rankers like 

Amit Ranjan

In this course we will be focussing on the preparations for UPSC mains for the optional paper Physics.

(Hindi) Mains Optional Physics - UPSC CSE

AFMC MBBS'06 AIR 44, NEET PG MDS AIR 20, Orthodontics, Facial Orthopedician, Qualified UPSC CSE Mains , Anthro Paper1-176, Adventure sport 

Mayank Jain

This course will help you to score high marks in interview by not repeating the mistakes which I did during my interview. It will cover the basics of interview, review of the board members, expected questions from economy , IR and social issue

(Hindi) UPSC Interview- Learn from my Mistakes

Kapil Sharma

(Hindi) l important Previous Years Question for UPPCS,RAS,MPPSC.UGC NET, SSC.CGL examination

Lessons

29 lessons • 6h 38m

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Rings and Subrings - Overview

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Rings- Part 1

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Rings - Part 2

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Rings- Part 3

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Ring - Part 4 (in Hindi)

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Ring - Part 5 (in Hindi)

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Rings - Part 6 (in Hindi)

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Rings - Part 7 (in Hindi)

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Rings Part- 8 (in Hindi)

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Ring - Part 9 (in Hindi)

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