Virendra's Classroom
Virendra's Classroom
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Presently Teaching (January 2022-May 2022)
Academic Calendar: Click Here
RING THEORY AND LINEAR ALGEBRA-I
Class Timings: Tuesday-Thursday (12-1 pm)
Platform: MSTEAMS & Offline Classes
ASSESS YOURSELF WITH OBJECTIVE QUESTIONS BASED ON BOOK BY Gallian, Joseph. A
For More Resources for Abstract Algebra: GO TO
Class Notes: To Download Class Notes Click Here
Video Lectures: To Watch Video Lectures Visit Our YouTube Channel (Online Learning)
Syllabus: Click Here
Course Objectives: The objective of this course is to introduce the fundamental theory of two objects, namely rings and vector spaces, and their corresponding homomorphisms.
Course Learning Outcomes:
The course will enable the students to:
Learn about the fundamental concept of rings, integral domains and fields.
Know about ring homomorphisms and isomorphisms theorems of rings.
Learn about the concept of linear independence of vectors over a field, and the dimension of a vector space.
Basic concepts of linear transformations, dimension theorem, matrix representation of a linear transformation, and the change of coordinate matrix.
References:
Gallian, Joseph. A. (2013). Contemporary Abstract Algebra (8th ed.). Cengage Learning India Private Limited. Delhi. Fourth impression, 2015.
Friedberg, Stephen H., Insel, Arnold J., & Spence, Lawrence E. (2003). Linear Algebra (4th ed.). PrenticeHall of India Pvt. Ltd. New Delhi.
NUMBER THEORY
Class Timings: Monday-Thursday (1-2pm)
Platform: MSTEAMS & Offline Classes
For More Resources for Abstract Algebra: GO TO
Class Notes: To Download Class Notes Click Here
Video Lectures: To Watch Video Lectures Visit Our YouTube Channel (Online Learning)
Syllabus: Click Here
Course Objectives: In number theory there are challenging open problems which are comprehensible at undergraduate level, this course is intended to build a micro aptitude of understanding aesthetic aspect of mathematical instructions and gear young minds to ponder upon such problems. Also, another objective is to make the students familiar with simple number theoretic techniques, to be used in data security.
Course Learning Outcomes:
Learn about some fascinating discoveries related to the properties of prime numbers, and some of the open problems in number theory, viz., Goldbach conjecture etc.
Know about number theoretic functions and modular arithmetic.
Solve linear, quadratic and system of linear congruence equations.
Learn about public key crypto systems, in particular, RSA.
References:
Burton, David M. (2012). Elementary umber Theory (7th ed.). Mc-Graw Hill Education Pvt. Ltd. Indian Reprint.
Neville Robinns. (2007). Beginning umber Theory (2nd ed.). Narosa Publishing House Pvt. Limited, Delhi.
Jones, G. A., & Jones, J. Mary. (2005). Elementary umber Theory. Undergraduate Mathematics Series (SUMS). First Indian Print.
STATISTICAL SOFTWARE-R
Class Timings: Monday-Friday (9-10 AM &11-12 Noon)
Platform: MSTEAMS & Offline Classes
For More Resources for STATISTICAL SOFTWARE-R: GO TO
Class Notes & Study Materials: Click Here
Video Lectures: To Watch Video Lectures Visit Our YouTube Channel (Online Learning)
Syllabus: Click Here
Course Objectives: The purpose of this course is to help you begin using R, a powerful free software program for doing statistical computing and graphics. It can be used for exploring and plotting data, as well as performing statistical tests.
Course Learning Outcomes:
Be familiar with R syntax and use R as a calculator.
Understand the concepts of objects, vectors and data types.
Know about summary commands and summary table in R.
Visualize distribution of data in R and learn about normality test.
Plot various graphs and charts using R.
References:
Bindner, Donald & Erickson, Martin. (2011). A Student’s Guide to the Study, Practice, and Tools of Modern Mathematics. CRC Press, Taylor & Francis Group, LLC.
Gardener, M. (2012). Beginning R: The Statistical Programming Language, Wiley Publications.
R Software can be downloaded from: https://www.rstudio.com/products/rstudio/download/ or ps: //www.r-studio.com/
Past Teachings:
BMATH306: Group Theory-I
Class Timings: Monday-Thursday (1-2PM)
Platform: MSTEAMS
ASSESS YOURSELF WITH OBJECTIVE QUESTIONS BASED ON BOOK BY Gallian, Joseph. A
For More Resources for Abstract Algebra: GO TO
Class Notes: To Download Class Notes Click Here
Video Lectures: To Watch Video Lectures Visit Our YouTube Channel (Online Learning)
Syllabus: Click Here
Course Objectives: The objective of the course is to introduce the fundamental theory of groups and their homomorphisms. Symmetric groups and group of symmetries are also studied in detail. Fermat’s Little theorem as a consequence of the Lagrange’s theorem on finite groups.
Course Learning Outcomes: The course will enable the students to:
Recognize the mathematical objects that are groups, and classify them as Abelian, cyclic and permutation groups, etc.
Link the fundamental concepts of groups and symmetrical figures.
Analyze the subgroups of cyclic groups and classify subgroups of cyclic groups.
Explain the significance of the notion of cosets, normal subgroups and factor groups.
Learn about Lagrange’s theorem and Fermat’s Little theorem.
Know about group homomorphisms and group isomorphisms.
Books:
Gallian, Joseph. A. (2013). Contemporary Abstract Algebra (8th ed.). Cengage Learning India Private Limited, Delhi. Fourth impression, 2015.
Rotman, Joseph J. (1995). An Introduction to The Theory of Groups (4th ed.). Springer Verlag, New York.
Other books:
Rotman, Joseph J. (1995). An Introduction to The Theory of Groups (4th ed.). Springer Verlag, New York
David S. Dummit and Richard M. Foote, Abstract Algebra, 3rd Edition, published by Wiley
Fraleigh John B., A First Course in Abstract Algebra Ed.7, Pearson learning
LateX and HTML with Practical: Syllabus
LateX and HTML with Practical: Syllabus
Class Timings: Monday (9:30AM-10:30AM) & Friday (12:00NOON-1:00PM)
Platform: MSTEAMS
Syllabus: Click Here
Video Lectures: To Watch Video Lectures Visit Our YouTube Channel (Online Learning)
Course Objectives: The purpose of this course is to acquaint students with the latest typesetting skills, which shall enable them to prepare high quality typesetting, beamer presentation and webpages.
Course Learning Outcomes: After studying this course the student will be able to:
Create and typeset a LaTeX document.
Typeset a mathematical document using LaTeX.
Learn about pictures and graphics in LaTeX.
Create beamer presentations.
Create web page using HTML.
Books:
A STUDENT's GUIDE TO THE STUDY, PRACTICE, AND TOOLS OF MODERN MATHEMATICS: DONALD Bindner and Martin Erickson
Software Download
Online web for LaTeX Typesettings: https://www.overleaf.com/
LaTeX can be downloaded from: https://mirrors.tuna.tsinghua.edu.cn/ctex/legacy/2.9/
Notepad ++: https://notepad-plus-plus.org/downloads/
Complex Analysis :
Any subject, specially in Mathematical Sciences, easy to understand if we have some visualization for it. The same is true for the complex analysis too. A Visual and Interactive Introduction one may visit: www.complex-analysis.com
Other useful websites are:
http://archives.math.utk.edu/software/msdos/complex.variables/complex_analysis/
https://www.geogebra.org/m/Ni69jyKs
https://vankessel.io/visualizing-complex-functions
Knowing History behind the existence of a subject is one of the most interesting thing and thus with the complex Analysis. For
History of Complex Numbers Visit:
https://www.amazon.in/Imaginary-Tale-Princeton-Science-Library/dp/0691169241
https://www.math.uri.edu/~merino/spring06/mth562/ShortHistoryComplexNumbers2006.pdf
https://www.math.snu.ac.kr/~ckhan/mathhistory/complexhistory/complexhistory091008.pdf
Generic Elective (Calculus): Syllabus
Generic Elective (Calculus): Syllabus
Skill Enhancement Course (Statistical Software R): Syllabus
Skill Enhancement Course (Statistical Software R): Syllabus
Beginning R The Statistical Progamming Language: Mark Gardener
2. A STUDENT's GUIDE TO THE STUDY, PRACTICE, AND TOOLS OF MODERN MATHEMATICS: DONALD Bindner and Martin Erickson
R Software can be downloaded from: https://www.rstudio.com/products/rstudio/download/ or ps: //www.r-studio.com/
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