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July 4th, 2017, 10:19 PM  #1 
Senior Member Joined: Nov 2015 From: hyderabad Posts: 242 Thanks: 4  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/questionpapers.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, CauchyRiemann 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, HeineBorel 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 11:37 PM. 
July 4th, 2017, 10:40 PM  #2 
Senior Member Joined: Feb 2016 From: Australia Posts: 1,847 Thanks: 661 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?

July 4th, 2017, 10:53 PM  #3  
Senior Member Joined: Nov 2015 From: hyderabad Posts: 242 Thanks: 4  Quote:
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.  
July 5th, 2017, 11:06 AM  #4 
Senior Member Joined: Aug 2012 Posts: 2,424 Thanks: 759 
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 metaclue 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. Last edited by Maschke; July 5th, 2017 at 11:23 AM. 

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