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July 4th, 2017, 09:19 PM   #1
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Joined: Nov 2015
From: hyderabad

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Master's in Mathematics (M.Sc.)

Hello,

I am determined to get into one of the following two universities for Masters, namely, Chennai Mathematical Institute & Hyderabad Central University.

But for that I need to be strong with the foundations as well as in the advanced topics.

I have a year time to prepare for this, so please anyone who is good at preparing the study plan, help me.

I am providing the Entrance exam syllabus of both universities.

Since I'm not able to attach the pdfs here because of the size issue, I'm providing the link to look at the previous papers here:

HCU:
http://igmlnet.uohyd.ac.in:8000/question-papers.htm

(or)

http://igmlnet.uohyd.ac.in:8000/Entr...20-%202016.pdf

CMI:
Chennai Mathematical Institute

(or)

http://www.cmi.ac.in/admissions/samp...pgmath2016.pdf



CMI

Algebra
(a) Groups, homomorphisms, cosets, Lagrange’s Theorem, group actions, Sylow Theorems,
symmetric group Sn, conjugacy class, rings, ideals, quotient by ideals, maximal and prime
ideals, fields, algebraic extensions, finite fields
(b) Matrices, determinants, vector spaces, linear transformations, span, linear independence,
basis, dimension, rank of a matrix, characteristic polynomial, eigenvalues, eigenvectors,
upper triangulation, diagonalization, nilpotent matrices, scalar (dot) products, angle, rotations,
orthogonal matrices, GLn, SLn, On, SO2, SO3.

References:
(i) Algebra, M. Artin
(ii) Topics in Algebra, Herstein
(iii) Basic Algebra, Jacobson
(iv) Abstract Algebra, Dummit and Foote

Complex Analysis.
Holomorphic functions, Cauchy-Riemann equations, integration, zeroes of analytic functions, Cauchy formulas, maximum modulus theorem, open mapping theorem, Liouville’s theorem, poles and singularities, residues and contour integration, conformal maps, Rouché's theorem, Morera’s theorem

References:
(i) Functions of one complex variable, John Conway
(ii) Complex Analysis, L V Ahlfors
(iii) Complex Analysis, J Bak and D J Newman

Calculus and Real Analysis.
(a) Real Line: Limits, continuity, differentiability, Riemann integration, sequences, series, limsup,
liminf, pointwise and uniform convergence, uniform continuity, Taylor expansions,
(b) Multivariable: Limits, continuity, partial derivatives, chain rule, directional derivatives,
total derivative, Jacobian, gradient, line integrals, surface integrals, vector fields, curl, divergence,
Stokes’s theorem
(c) General: Metric spaces, Heine-Borel theorem, Cauchy sequences, completeness, Weierstrass
approximation.

References:
(i) Principles of mathematical analysis, Rudin
(ii) Real Analysis, Royden
(iii) Calculus, Apostol

Topology
Topological spaces, base of open sets, product topology, accumulation points, boundary,
continuity, connectedness, path connectedness, compactness, Hausdorff spaces, normal spaces,
Urysohn’s lemma, Tietze extension, Tychonoff’s theorem,

References:
Topology, James Munkres


HCU

Sets, sequences, series, limits, continuity, differentiation, integration, graphs of functions, coordinate geometry of two and three dimensions, group theory, vector spaces, matrices, determinants, linear transformations, rank, nullity, eigenvalues, system of linear equations, elementary probability, distribution theory and logical reasoning.


Thank you so much for your help. I'm looking forward.

Last edited by skipjack; July 4th, 2017 at 10:37 PM.
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July 4th, 2017, 09:40 PM   #2
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From: Australia

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Math Focus: Yet to find out.
Seems you already have a fairly extensive outline of topics.. What sort of plan do you expect someone to provide? A list of all the topics that you should study in a certain order?
Joppy is offline  
July 4th, 2017, 09:53 PM   #3
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Joined: Nov 2015
From: hyderabad

Posts: 206
Thanks: 2

Quote:
Originally Posted by Joppy View Post
Seems you already have a fairly extensive outline of topics.. What sort of plan do you expect someone to provide? A list of all the topics that you should study in a certain order?
I actually want to know with which topic I should start and also want to know which books I should refer for the basic and advance topics.

I need a plan through which I can assure my self that I have learned enough skills and I am capable of getting into those universities.

I'm very interested in Mathematics but my problem is that I forget those which i learnt in my graduation after it has completed. So now I want to focus more on getting life skills which I should remember and shouldn't forget which can only possible if we are completely strong in basics.

So, please someone help me with the above things. Thanks.
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July 5th, 2017, 10:06 AM   #4
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Joined: Aug 2012

Posts: 1,527
Thanks: 364

I have a specific suggestion. In general when you've posted questions from sample tests, they're multiple choice and once you're told that the answer is A or C or whatever, that's the end of it.

I've never seen you write out a complete mathematical argument from start to finish. Premises, reasoning, conclusion.

In grad school that is ALL you do. Definition, theorem, proof. Over and over. Prove this, prove that. Or even harder, "prove or disprove," which takes away the meta-clue that the given statement is either true or false. You have to play with counterexamples and proofs till you see what's going on.

I would strongly urge you to challenge yourself to write complete, clear mathematical arguments for every problem you solve or see the solution to. Once you get to grad school that will be expected of you.
Thanks from Country Boy and Joppy

Last edited by Maschke; July 5th, 2017 at 10:23 AM.
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