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Composition of Mathematics Courses intended for the UG Program

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Name of the courses being offered by the Department of mathematics

you

Analysis and Linear

Algebra

2

Examination and Geradlinig

Algebra

three or more

Probability and

Statistics

four

Multivariable Calculus

and Complicated Variable

Primary Algebra and

Number Theory

Elective

Elective

5

Algebra I

Linear Algebra

Evaluation I

Topology I

6

Analysis 2

Complex Evaluation

ODE

Optional

7

Algebraic Topology I

Functional Analysis

PDE

almost 8

Elective

Optional

Project

Electives include:

Algebra II, Galois Theory, Possibility, Harmonic Research, Lie Teams, Commutative Algebra, Numerical Evaluation, Number Theory.

Detailed Syllabus:

Analysis and Linear Algebra I:

One-variable calculus: Real and Intricate numbers; Convergence of sequences and series; Continuity, advanced value theorem, existence of maxima and minima; Difference, mean value theorem, The singer series; Integration, fundamental theorem of Calculus, improper integrals. Linear Algebra: Vector places (over real and intricate numbers), basis and dimensions; Linear Conversions and matrices; Determinants.

Recommendations:

Apostol, Calculus, Volume I, 2nd. Model, Wiley, India, 2007. G. Strang, Geradlinig Algebra As well as Applications, 4th Edition, Brooks/Cole, 2006

Research and Geradlinig Algebra:

Geradlinig Algebra continuing: Inner products and Orthogonality; Eigenvalues and Eigenvectors; Diagonalisation of Symmetric matrices.

Multivariable calculus: Functions in $\R^n$; Incomplete and Total derivatives; Sequence rule; Dicho, minima and saddles; Lagrange multipliers; Integration in $\R^n$, change of variables, Fubini's theorem; Gradient, Divergence and Curl; Collection and Surface integrals in $\R^2$ and $\R^3$; Stokes, Green's and Divergence theorems.

Introduction to Normal Differential Equations; Linear Ballade and Canonical forms to get linear changes.

References:

Big t. M. Defensor, Calculus, Volume II, second. Edition, Wiley Wiley India, 2007. G. Strang, Thready Algebra As well as Applications, 4th Edition, Brooks/Cole, 2006 Meters. Artin, Algebra, Prentice Corridor of India, 1994.

M. Hirsch, S. Smale, 3rd there’s r. L. Devaney, Differential Equations, Dynamica lSystems, and an Introduction to Damage, 2nd Edition, Academic Press, 2004.

Probability and Statistics:

Basic symbole of probability, conditional probability and independence, Bayes' theorem, random parameters and distributions, expectation and variance, conditional expectation, moment generating features, limit theorems.

Samples and sampling distributions, estimations of parameters, testing of ideas, regression, relationship and examination of difference.

Reference:

L. L. Meyer, Introductory Probability and Record Applications, Addison-Wesley, 1970 3rd there’s r. V. Hogg and Elizabeth. A. Tanis, Probability and Statistical Inference, 2004, Pearson Education Inc., Delhi, 6th Edition.

L. V. Hogg and T. Ledolter, Anatomist Statistics, 1987, Macmillan Submitting Company, New york city.

S. Ross, A First Training course in Probability, 2004, Pearson Education Incorporation., Delhi, 6th Edition. Multivariable Calculus and Complex Varying:

Review of total derivatives, inverse and acted function theorem; Complex linearity and the CauchyRiemann equations; Complex functions, conformal mappings. Multilinear forms on vector spots; Tensor companies symmetric items; Alternating varieties and the external algebra of any vector space.

Differential forms, integration upon chains, Stokes theorem intended for differential forms; Complex integration and Cauchy's theorem; Power series and Laurent series representations; Residue theorem and Contour the use; Harmonic features.

References:

Capital t. M. Defensor, Calculus, Volume II, second. Edition, Wiley India, 2007. T. W. Gamelin, Complex Analysis, Springer Undergraduate Text messages in Math concepts, Springer Intercontinental Edition, 2006

Elementary Algebra and Quantity Theory:

Divisibility and Euclid's algorithm, Fundamental theorem of...

References: Garabedian, P. 3rd there’s r., Partial Gear Equations, Ruben Wiley and Sons, 1964.

Prasad. L. and Ravindran, R., Partial Differential Equations, Wiley Eastern, 1985.

Renardy, M. and Rogers, L. C., An intro to Partially Differential Equations, SpringerVerlag, 1992.

Fritz Steve, Partial differential box Equations, Springer (International Learners Edition), the year of 1971.

22.08.2019