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Available courses

BSc Mathematics-Semester V (Core): Elementary Abstract Algebra

Elementary Abstract Algebra (B.Sc. V, Core – MAT-001-CC-3510)

Course Description:
This course introduces the foundations of abstract algebra, covering relations, binary operations, permutations, groups, and rings. Students will explore Lagrange’s theorem, quotient groups, group homomorphisms, and Cayley’s theorem. The course balances theoretical rigor with problem-solving applications, preparing students for advanced studies in algebra and its applications.

Learning Outcomes:

  • Identify and work with groups, rings, and fields.

  • Analyze and apply algebraic properties in solving problems.

  • Use homomorphisms and isomorphisms to study structural similarities.

  • Apply abstract algebra in real-world contexts.

BSc Semester V:LaTeX: MAT-001-CC-3540

LaTeX (B.Sc. V, Core – MAT-001-CC-3540)

Course Description:
This skill-based course equips students with the ability to prepare professional mathematical and scientific documents using LaTeX. Topics include typesetting text and mathematical expressions, creating structured documents, and preparing graphics and presentations with Beamer. By the end of the course, students will be confident in writing reports, assignments, and research articles in LaTeX.

Learning Outcomes:

  • Create and typeset documents using LaTeX.

  • Typeset mathematical formulas and symbols effectively.

  • Insert graphics and prepare professional Beamer presentations.

Minor Course for BSc Semester III

This Minor Core course is designed for students from disciplines such as Chemistry, Physics, and related sciences who wish to build a strong foundation in abstract mathematical thinking.

The course introduces essential algebraic structures and their applications, aiming to develop logical reasoning and structural understanding relevant across scientific fields; Groups and subgroups, cyclic groups, normal subgroups, and quotient groups; Group homomorphisms, properties and fundamental theorem of homomorphisms, isomorphisms; Rings, subrings, ideals, quotient rings, integral domains, division rings, and fields; Vector spaces, subspaces, linear combinations, span, linear independence, basis and dimension, and linear transformations.

This course serves as a mathematical bridge for students of diverse backgrounds to appreciate the structural beauty and utility of algebra in their own disciplines.

MAT-DE-351: Discrete Mathematics for BSc 5th Semester (CBCS)

Course Objectives

The course aims to introduce the concepts of ordered sets, lattices, sublattices, and homomorphism between lattices. It also includes an introduction to modular and distributive lattices and Boolean algebra. It further includes an introduction to graph theory.

Course Learning Outcomes

After completing this course, students will be able to:

  1. Understand the notion of ordered sets.

  2. Learn about lattices, modular and distributive lattices, sublattices, and homomorphism between lattices.

  3. Become familiar with Boolean algebra, Boolean homomorphism.

  4. Get acquainted with the basics of graph theory.

Course Format and Content

  • Unit I: Mathematical Induction, Principle of Inclusion and Exclusion, Pigeonhole Principle, Generating Functions, Partitions, Recurrence Relations, Generating Functions from Recurrence Relations.

  • Unit II: Partial Ordering, Properties of Ordered Sets, Order Isomorphism, Hasse diagrams, Dual of an ordered set, Duality principle, Maximal and minimal elements, Lattices, Sublattices, Products and homomorphisms, modular and distributive lattices.

  • Unit III: Boolean Algebras, De Morgan's laws, Boolean homomorphism, Boolean function, Sum of product and Product of Sums form, Normal form and canonical form, Logic gates and Logic Circuits.

  • Unit IV: Graphs: Basic concepts, subgraph, walk, path, circuits, Connectedness, complete graph, Bipartite graphs, Isomorphism in Graphs, Trees, spanning trees, weighted graph and shortest spanning tree.

ELementary LInear Algebra: MAT-001-CC-2320

​Course Title
​MAT-001-CC-2320 ELEMENTARY LINEAR ALGEBRA
​Course Credit
​4 (L-3, T-1, P-0)
​Total Contact Hours
​60
​Assessment
​Theory: 100 (End Semester: 80, Internal Assessment: 20)
​Course Outcomes
​Upon successful completion of this course, students will be able to:
​CO1: Learn about the concept of linear independence and dependence of vectors over a field, basis and the dimension of a vector space.
​CO2: Basic concepts of linear transformations and matrix representation of a linear transformation.
​CO3: Concepts of characteristic polynomial, eigenvalues, eigenvectors, and eigenspaces.
​CO4: Learn about the concept of linear functional and dual space.
​Course Units
​Unit-I: Vector Spaces (Contact Hours: 15)
​Vector spaces, subspaces, algebra of subspaces, quotient spaces, linear combination of vectors, linear span, linear independence, basis and dimension, dimension of subspaces, linear sums and direct sums.
​Unit-II: Linear Transformations (Contact Hours: 20)
​Linear transformations, null space, range, rank and nullity of a linear transformation, dimension theorem, singular and non-singular linear transformations and isomorphism, algebra of linear transformations, matrix representation of a linear transformation and change of basis matrix.
​Unit-III: Characteristic Polynomial of Matrices (Contact Hours: 15)
​Characteristic polynomial of matrices, eigenvalues and eigenvectors, diagonalization. Cayley-Hamilton theorem and its use in finding the inverse of a matrix.
​Unit-IV: Linear Functional (Contact Hours: 10)
​Linear functional, Dual Space, Dual Basis, Double dual, Annihilators and Transpose of a linear mapping.
​Recommended Books
​K. Hoffman and R. A Kunze, Linear Algebra, 2nd Ed., Prentice-Hall of India Pvt. Ltd., (2015).
​S. Lipschutz, Beginning Linear Algebra, McGraw Hill (2020).
​Gilbert Strang, Linear Algebra And Its Application, Cengage Learning India (2005).
​S. K. Mapa, Higher Algebra: Abstract and Linear, Levant Books India (2020).

Linear Algebra: 5th Semester (CBCS)