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(Re – Accredited with ‘A’ Grade by NAAC) DEPARTMENT OF MATHEMATICS B.Sc. MATHEMATICS COURSE STRUCTURE (w.e.f. 2011 – 2014 batch onwards) Semester – I
Semester – II
Semester – III
Semester – IV
Semester – V
Semester – VI
List of Non Major Elective papers (NME) (2 Hours /week) 1) Mathematical Aptitude for competitive Examinations (For semester – III) 2) Mathematical Logic (For semester – IV) List of Elective papers (5 Hours / week) (One elective paper to be chosen in each of III, IV and V semester) 1) Analytical Geometry of 3D and Vector Calculus 2) Financial Accounting and Costing 3) Stochastic Processes 4) Data Structures 5) Fuzzy sets 6) Computer Algorithms 7) Data Mining 8) Mathematical Modelling List of Skill Based Elective papers (SBE) (2 Hours / week) 1) C  Programming – Practical 2) Numerical Methods – Practical 3) Graph Theory – Practical 4) Theory of Numbers 5) Theory of Matrices 6) Statistical Test of Significance 7) Z and Fourier Transforms 8) Theory of Lattices 9) Data Structures  Practical 10) Personality Development Self study paper: History of Mathematics A) Consolidation of Contact Hours and Credits : UG
B) Curriculum Credits : Part wise Part – I 12 Credits Part – II 12 Credits Part – III Core 60 Credits Allied 20 Credits Elective 15 Credits 95 Credits Part – IV NME (2 x 2) 04 Credits SBE (6 x 2) 12 Credits VE 02 Credits ES 02 Credits 20 Credits Part – V 01 Credits 140 Credits THIAGARAJAR COLLEGE (AUTONOMOUS), MADURAI – 625 009 (Re Accredited with 'A' Grade by NAAC) Department of Mathematics (From 2011 – 2014 batch onwards) Course : B.Sc. Code No. : MM11 Semester : I No. of hours allotted : 5 Paper : Core 1 No. of credits : 4 Title of the Paper : Differential Calculus Course objective: To develop problem solving skills and study the applications of differential calculus Unit  I (18 Hours) Continuous functions – Algebra of continuous functions – Types of discontinuities – Properties of continuous functions  Differentiability  Algebra of derivatives – Derivatives of standard functions  The Chain rule for differentiation  Differentiation of inverse function  n^{th} derivative of some standard functions. Unit  II (15 Hours) Leibnitz's theorem for n^{th} derivative of a product  Partial derivatives – Homogeneous functions and Euler’s theorem. Unit  III (15 Hours) Multiple points of a curve  Asymptotes  Method of finding asymptotes for the curve y = f(x)  Method of finding asymptotes for the curve f(x, y)= 0. Unit  IV (12 Hours) Curvature  Evolute  Envelope. Unit  V (15 Hours) Maxima and minima of functions of two variables  Lagrange's method of Undermined multipliers. Text Books : 1) Calculus, Arumugam and Issac, New Gamma publishing House, Edition 1995 2) Calculus – Volume I, S. Narayanan, T.K. Manicka Vasagam Pillay, S. Viswanathan Pvt. Ltd., Edition 1997
Reference Book : Differential Calculus, Shanti Narayan, S. Chand and Company Ltd., 14^{th} Edition, Reprint 2002 THIAGARAJAR COLLEGE (AUTONOMOUS), MADURAI – 625 009 (Re Accredited with 'A' Grade by NAAC) Department of Mathematics (From 2011 – 2014 batch onwards) Course : B.Sc. Code No. : MM12 Semester : I No. of hours allotted : 5 Paper : Core 2 No. of credits : 4 Title of the Paper : Statistics Course objective: To acquire various skills about basic statistical concepts and to know fitting statistical data in various distributions. Unit  I (15 Hours) Measures of Dispersion : Introduction – Measures of Dispersion. Moments Skewness and Kurtosis : Introduction – Moments – Skewness and Kurtosis. Unit  II (15 Hours) Correlation and Regression : Introduction – Correlation – Rank Correlation – Regression – Correlation Coefficient for a Bivariate Frequency Distribution. Unit  III (15 Hours) Random Variables : Introduction – Random Variables – Discrete Random Variable – Continuous Random Variable – Mathematical Expectations – Mathematical Expectation of Continuous Random Variable – Moment Generating Function – Characteristic Function. Unit  IV (15 Hours) Some Special Distributions : Introduction – Binomial Distribution – Poisson Distribution – Normal Distribution – Some More Continuous Distributions (Gamma Distribution, Chi – Square Distribution, Student’s tDistribution, Snedecor’s FDistribution, Fischer’s ZDistribution). Unit  V (15 Hours) Tests of Significance (Small Samples) : Introduction – Test of Significance Based on t – Distribution – Test of Significance Based on FTest. Test Based on ChiSquare Distribution: Introduction – ChiSquare Test for Population Variance – ChiSquare Test to test the goodness of fit. Text Book Statistics  S. Arumugam and A. Thangapandi Isaac, New Gamma Publishing House, June 2007
Reference Books : 1. Fundamentals of Mathematical Statistics  S. C. Gupta and V.K. Kapoor, Sultan Chand & Sons, 9^{th} Edition. 2. Statistical methods  Dr. S. P. Gupta  Sultan Chand and Sons, 25^{th} thoroughly revised and enlarged edition, New Delhi – 110 002 THIAGARAJAR COLLEGE (AUTONOMOUS), MADURAI – 625 009 (Re Accredited with 'A' Grade by NAAC) Department of Mathematics (From 2011 – 2014 batch onwards) Course : B.Sc. Code No. : MM13 Semester : I No. of hours allotted : 4 Paper : Core 3 No. of credits : 4 Title of the Paper : Algebra Course objective:
Unit –I (12 Hours) BINOMIAL THEOREM : Binomial theorem for a rational index – Some important particular cases of binomial expansion – sign of terms of a binomial expansion – Numerically greatest term – Expansion by splitting the term by Partial fractions – Application to Summation of series Unit II (12 Hours) EXPONENTIAL AND LOGARITHMIC SERIES : Exponential limit – Exponential theorem – summation of series – Expansion in two ways – Logarithmic series theorem – Modification of log series – Differents forms – Euler’s constant  summation of series Unit – III (12 Hours) THEORY OF EQUATIONS : ransformations of equations – Construction of new equations from the given ones, Reciprocal equations, Descartes rule of signs and Multiple roots Unit – IV (12 Hours) CONTINUED FRACTIONS : Definitions – Recurring continued fractions – law of formation of the successive convergents – Properties of convergents Unit – V (12 Hours) INEQUALITIES : Inequalities – Elementary properties – Arithmetic mean – Geometric mean – Weierstrass inequality – Cauchy inequality Text Books: 1. Algebra  Vol – 1 T.K.M Pillay and others, S. Viswanathan (printers and publishers), 2008 2. Algebra –Vol – 2 T.K.M Pillay and others, S. Viswanathan (printers and publishers), 2008
Reference Book: Algebra  S. Arumugam and Issac, New Gamma publications, 1995 THIAGARAJAR COLLEGE (AUTONOMOUS), MADURAI – 625 009 (Re Accredited with 'A' Grade by NAAC) Department of Mathematics (From 2011 – 2014 batch onwards) Course : B.Sc. Code No. : MM21 Semester : II No. of hours allotted : 5 Paper : Core 4 No. of credits : 4 Title of the Paper : Integral Calculus Course objective: To develop problem solving skills in Calculus and study the applications of integral calculus Unit  I (18 Hours) Integration by parts  Bernouilli's formula  Reduction formula  Improper integrals  Some tests for convergence of improper integrals  Evaluation of some improper integrals. Unit  II (18 Hours) Double integral  Evaluation of double integral  Triple integral  Jacobians  Change of variables in double and triple integrals. Unit  III (12 Hours) Beta and Gamma functions  Properties and results involving Beta and Gamma functions. Unit  IV (15 Hours) Area as double integral  Volume as triple integral  Area of surface. Unit  V (12 Hours) Centre of mass  Moment of inertia. Text Book : Calculus volume II  Arumugam and Issac, New Gamma publishing House, Edition 1990
Reference Book : Integral Calculus, Shanti Narayan, S. Chand and Company Ltd., 9^{th} Edition, Reprint 2002 THIAGARAJAR COLLEGE (AUTONOMOUS), MADURAI – 625 009 (Re Accredited with 'A' Grade by NAAC) Department of Mathematics (From 2011 – 2014 batch onwards) Course : B.Sc. Code No. : MM22 Semester : II No. of hours allotted : 5 Paper : Core 5 No. of credits : 4 Title of the Paper : Differential Equations and its Applications Course objective: 1. To expose the students to various methods of solving different kinds of differential equations. 2. To expose the students how to apply their knowledge in Differential Equations to other branches of Sciences. Unit – I (15 Hours) Differential Equations of First Order : Differential Equation – Equations of first order and first degree – Exact differential Equations – Integrating factors – Linear equations – Bernouilli’s equations – Equations of first order and higher degree. Unit – II (15 Hours) Linear Equations of Higher order : Linear equations with constant coefficients – Method of finding complementary functions – Method of finding particular integral  Homogeneous linear equations – Linear equations with variable coefficients – Simultaneous linear differential equations – Total differential equations  Method of variation of parameters  Removal of first derivative. Unit – III (15 Hours) Laplace Transform : Laplace transform – Inverse Laplace transform – Solution of differential equation using Laplace transform. Unit – IV (15 Hours) Partial Differential Equations : Formation of partial differential equations – First order partial differential equations – Methods of solving first order partial differential equations – Some standard forms – Charpit’s Method. Unit – V (15 Hours) Applications of Differential Equations : Orthogonal trajectories – Growth and decay – Continuous compound interest – The Brachistochrone problem – Simple electric circuits – Falling bodies – Simple harmonic motion – Central forces – Planetary motion. Text Book: Differential Equations and Applications – Arumugam & Isaac, New Gamma Publishing House – 2008.
Reference Book Differential Equations and its Applications– S. Narayanan and T. K. ManicavachagamPillay, S. Viswanathan (printers & publishers) Pvt. Ltd., 1996 THIAGARAJAR COLLEGE (AUTONOMOUS), MADURAI – 625 009 (Re Accredited with 'A' Grade by NAAC) Department of Mathematics (From 2011 – 2014 batch onwards) Course : B.Sc. Code No. : MM23 Semester : II No. of hours allotted : 4 Paper : Core 6 No. of credits : 4 Title of the Paper : Sequences, Series and Trigonometry Course objective: 1.To introduce the convergency and divergency of sequences and series 2.To introduce the trigonometric functions Unit  I (12 Hours) Sequences – Bounded sequences – monotonic sequences – convergent sequences  divergent and oscillating sequences – Algebra of limits. Unit  II (12 Hours) Behaviour of Monotonic Sequences  Some theorems on limits – Subsequenes – Limit points – Cauchy sequences – The upper and lower limits of a sequence. Unit  III (12 Hours) Infinite Series – Comparison Test – Kummer’s Test – Root Test and Condensation Test – Integral Test. Unit  IV (12 Hours) Alternating series – Absolute Convergence – Tests for Convergence of Series of arbitrary terms Rearrangement of Series – Multiplication of series – Power series. Unit  V (12 Hours) Expression for sin nθ, cos nθ, tan nθ, sin^{n} θ, cos^{n} θ – Expansion of sin θ , cos θ, tan θ in powers of θ  Hyperbolic functions   Inverse Hypeerbolic functions Text Books: 1) Sequences and Series  Arumugam and Issac, New Gamma Publishing House, 1997 2) Trigonometry and Fourier Serie  Arumugam, Issac and Somasundaram, New Gamma Publishing House, 1997
Reference Books : 1. Algebra Volume I  T.K.M. Pillai, T. Natarajan and K.S. Ganapathy S. Viswanathan Publishers, 2008 2. Trigonometry  S. Narayanan and T.K. Manickavachagom Pillay S. Viswanathan Publishers, 1986 THIAGARAJAR COLLEGE (AUTONOMOUS), MADURAI – 625 009 (Re Accredited with 'A' Grade by NAAC) Department of Mathematics (From 2011 – 2014 batch onwards) Course : B.Sc. Code No. : MM31 Semester : III No. of hours allotted : 5 Paper : Core 7 No. of credits : 4 Title of the Paper : Modern Analysis Course objective: To acquire knowledge in countable and uncountable sets, inequalities, Metric spaces, continuity, completeness and connectedness of metric spaces. Unit  I (15 Hours) Preliminaries: Sets and Functions – Countable sets – Uncountable sets – Inequalities of Holder and Minkowski. Unit  II (15 Hours) Metric Spaces : Definitions and Examples – Bounded Sets in a Metric Space – Open Ball in a Metric Space – Open Sets – Subspaces – Interior of a Set – Closed Sets – Closure – Limit Point – Dense Sets. Unit  III (15 Hours) Complete Metric Space and Continuity : Introduction – Completeness – Baire’s Category Theorem  Continuity – Homeomorphism – Uniform Continuity – Discontinuous Functions on R. Unit – IV (15 Hours) Connectedness: Introduction –Definition and Examples – Connected Subsets of R – Connectedness and Continuity. Unit  V (15 Hours) Compactness: Introduction – Compact Space – Compact Subset of R – Equivalent Characterization for Compactness – Compactness and Continuity. Text Book: Modern Analysis  S. Arumugam and A. Thangapandi Isaac, New Gamma Publishing House, 1997
Reference Book : Methods of Real Analysis  Goldberg, Oxford and IBH publishing Company, 1964. THIAGARAJAR COLLEGE (AUTONOMOUS), MADURAI – 625 009 (Re Accredited with 'A' Grade by NAAC) Department of Mathematics (From 2011 – 2014 batch onwards) Course : B.Sc. Code No. : MM41 Semester : IV No. of hours allotted : 5 Paper : Core 8 No. of credits : 4 Title of the Paper : Modern Algebra Course objective: To study the theory related with theorem so that the students may copeup with the higher studies in Algebraic systems Unit  I (18 Hours) Group  Elementary properties of a group  Permutation groups  Subgroups  Cyclic groups  Cosets and Lagrange's theorem. Unit  II (15 Hours) Normal subgroups  Isomorphism  Automorphism  Homomorphism. Unit  III (15 Hours) Ring  Properties of Rings  Isomorphism  Types of Rings  Characteristic of a Ring  Ideals  Quotient Rings  Maximal and Prime ideals  Homomorphism of Rings. Unit  IV (15 Hours) Field of quotients of an integral domain  Ordered integral domain  U.F.D.  Euclidean domain. Unit  V (12 Hours) Vector space  Subspace  linear transformation  Linear span  Linear independence  Basis and dimension  Inner product spaces  Orthogonality. Text Book: Modern Algebra  S. Arumugam and A. Thangapandi Isaac New Gamma Publishing House, 1996
Reference Book: Topics in Algebra I.N. Herstein, Wiely India Pvt. Ltd, II Edition, Reprint 2007 THIAGARAJAR COLLEGE (AUTONOMOUS), MADURAI – 625 009 (Re Accredited with 'A' Grade by NAAC) Department of Mathematics (From 2011 – 2014 batch onwards) Course : B.Sc. Code No. : MM51 Semester : V No. of hours allotted : 5 Paper : Core 9 No. of credits : 4 Title of the Paper : Mechanics 