B.Sc. Mathematics
1st Semester Syllabus
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MJC-01 : Algebra
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Unit 1: Complex Numbers and Trigonometry
◦Polar representation of complex numbers
◦De-Moivre's theorem and its applications
◦Logarithms of complex quantities
◦Hyperbolic functions
◦Gregory series
◦Summation of series
◦Resolution into factors
Unit 2: Set Theory and Relations
◦Cartesian product of sets
◦Equivalence relations
◦Partition
◦Partial and total order relation
◦Functions
◦Composition of functions
◦Invertible functions
◦Cardinality of a set
◦Countable and Uncountable sets
◦Cantor's theorem
Unit 3: Number Theory
◦Well-ordering property of positive integers
◦Division algorithm
◦Euclidean algorithm
◦Fundamental Theorem of Arithmetic
◦Modular arithmetic and basic properties of congruences
◦Principle of mathematical induction
Unit 4: Matrices and Linear Equations
◦Matrices
◦Operation on Matrices
◦Kinds of matrices
◦Transpose
◦Symmetric & skew symmetric Matrices
◦Hermitian
◦Skew Hermitian Matrices
◦Adjoint and Inverse of a matrix
◦Orthogonal matrix
◦Solution of a system of linear equations by matrix methods
◦Echelon forms
◦Rank of a matrix
Reference Books:
- Dickson, Leonard Eugene (1922). First Course in The Theory of Equations. John Wiley & Sons, Inc. New York
- Kolman, Bernard, & Hill, David R. (2001). Introductory Linear Algebra with Applications (7th ed.). Pearson Education, Delhi. First Indian Reprint 2003
- Andrilli, Stephen, & Hecker, David (2016). Elementary Linear Algebra (5th ed.). Academic Press, Elsevier India Private Limited
- Burton, David M. (2007). Elementary Number Theory (7th ed.). Tata Mc-Graw Hill Edition, Indian Reprint
- K.K.Jha, Advanced Set Theory. Nav Bharat Prakashan Patna
- M.L.Khanna, Theory of Equations, Jai Prakash Nath & Co. Merrut (U.P.)
- Lalji Prasad, Matrices, Paramount Publications Patna
- Dasgupta, Trigonometry, Bharti Bhawan Patna