BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE, Pilani
Pilani Campus
AUGS/ AGSR Division
FIRST SEMESTER 2022-2023
Course Handout
Dated: 29/08/2022
In addition to part-I (General Handout for all courses appended to the timetable) this portion gives
further specific details regarding the course.
Course No. : MATH F215
Course Title : ALGEBRA I
Instructor-in-charge : JITENDER KUMAR
1. Scope and Objective of the Course:
The objective of this course is to teach the importance of fundamental algebraic
structures in modern mathematics and to relate the general results so obtained to concrete
applications.
2. Textbook: I.N. Herstein: Topics in Algebra, 2nd ed., John Wiley (1999)
3. Reference Books:
1. Michael Artin: Algebra, 1st edition, Prentice Hall of India (1991)
2. John B. Fraleigh: A First Course in Abstract Algebra, 7th edition, Pearson (2003)
3. David S. Dummit & Richard M. Foote: Abstract Algebra, 2nd edition, John Wiley (1999).
4. Joseph Gallian: Contemporary Abstract Algebra, 8th edition, Brooks/Cole, Cengage learning
(2012).
Please Do Not Print Unless Necessary
BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE, Pilani
Pilani Campus
AUGS/ AGSR Division
4. Course Plan
Module Number Lecture session Sections Learning Outcome
1. Introduction to Group, L1.1-1.3 Definition and Examples of 2.1, 2.2 Understanding the
structure and their properties Groups concept of a group
L1.4. Preliminary Lemmas 2.3
2. Introduction to L2.1-2.2 Subgroups 2.4 Concept of subgroup
subgroups and a special class has more implications
of subgroups L2.3 A Counting Principle 2.5 than a subset.
L2.4 -2.5 Normal subgroups 2.6 Generalization of
modular arithmetic to
L 2.6 Quotient groups
arbitrary groups
3. Structure preserving maps L3.1 -3.2 Homomorphisms 2.7 Which re-labeling of
between two groups group elements is
L3.3 Automorphisms 2.8 allowed?
4. Abstract groups are not L4.1 Cayley’s theorem 2.9 To learn how to
that abstract after all extend group structure
to finite permutation
groups and
applications of
Cayley’s theorem
5. An important group in L5.1-5.3 Permutation Groups 2.10 Knowledge about the
algebra permutation group and
its subgroups
6. Introduction to class L6.1-6.2 Another counting principle 2.11 To learn applications
equation of a group, their of class equation. Able
applications and Sylow's L6.3-6.4 Sylow’s theorems 2.12 to apply Sylow
theorems theorems to analyze
the structure of groups
and to rule out
existence of simple
groups of certain
orders
7. Introduction to Ring L7.1 Definition & Examples of Rings 3.1 Basic concepts of a
structure ring
L7.2 Ring of real Quaternions 3.2
Please Do Not Print Unless Necessary
BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE, Pilani
Pilani Campus
AUGS/ AGSR Division
8. Structure preserving maps L8.1-8.2 Homomorphisms 3.3 Which maps between
between two ring structure rings relate their
structures?
9. Construction of Quotient L9.1-9.3 Ideals and Quotient rings 3.4, 3.5 To learn modular
rings and their properties arithmetic in rings
10. Important rings in L11.1-11.5 Euclidean rings and 3.7, 3.8 Algebraic properties
algebra Principal Ideal Rings of these rings,
examples,
L11.6-11.7 Polynomial rings 3.9 irreducibility of
polynomials over a
field and construction
of a field
11. Rings in which L12.1- 12.4 Factorization of 3.10, 3.11 Irreducibility of
factorization is a reliable polynomials, Unique Factorization polynomials with
process Domains rational coefficients,
algebraic properties of
unique factorization
domain
*In tutorial classes, practice problems will be discussed on the topics covered in previous
lectures.
5. Evaluation Scheme:
Evaluation Components Weightage (%) Time Date of Evaluation Nature of
(Minutes) Component
1 Midsemester Exam 35% 90 As per Timetable Closed/Open
Book
2 20% TBA TBA Closed Book
Quizzes
3 Comprehensive Exam 45% 180 As per Timetable Closed/Open
Book
Please Do Not Print Unless Necessary
BIRLA INSTITUTE OF TECHNOLOGY AND SCIENCE, Pilani
Pilani Campus
AUGS/ AGSR Division
Upon Successful completion of MATH F215 Algebra 1 student should be able to:
(i) Assess properties implied by the definitions of groups and rings,
(ii) Use of various canonical types of groups (including cyclic groups and groups of permutations)
and canonical types of rings (including Polynomial rings, Euclidean rings and Principal ideal rings),
(iii) Analyze and demonstrate examples of subgroups, normal subgroups and quotient groups,
(iv) Analyze and demonstrate examples of ideals and quotient rings,
(v) Use the concepts of isomorphism and homomorphism for groups and rings, and
(vi) Produce rigorous proofs of results (theorems, propositions, and lemmas) arising in the context
of abstract algebra.
6. Chamber Consultation Hour: Saturday, 12.00-12.50 PM.
7. Notices: All notices regarding MATH F215 will be displayed on NALANDA.
8. Makeup: Prior permission is needed for makeup; makeup will only be given if enough evidence
is there for not being able to take Midsem/Compre. Quizzes will not have any make-ups.
(Jitender Kumar)
Instructor In charge; MATH F215
Please Do Not Print Unless Necessary
