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Real Analysis: Short Questions and MCQs @msc:mcqs_short_questions
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thor of this page is Dr. [[:atiq]]. The page will be updated periodically. </callout> ===== Short questions ===== - What is the difference between rational and irrational numbers? - Is there a rational number exists between any two rational numbers. - Is there a real number
Syllabus for UoS (Private only) @msc:syllabus
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a. <WRAP center round alert 90%> The syllabus has been changed and few optional subjects has been dropped. Please be alert --- // 2017/08/25 17:05// </WRAP> ===== Eligibility ===== The candidate ... hree courses are compulsory and the students will be required to choose three more courses from the li
Chapter 01 - Real Number System @msc:real_analysis_notes_by_syed_gul_shah
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====== Chapter 01 - Real Number System ====== ==== Contents & Summary ==== * Theorem: There is no r... l //p// such that $p^2=2$. * Theorem: Let //A// be the set of all positive rationals //p// such that... uch that $p^2<2$ then //A// contain no largest member and //B// contains no smallest member. * Order on a set. * Ordered set. * Bound. * Least upp
Chapter 02 - Sequence and Series @msc:real_analysis_notes_by_syed_gul_shah
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c Sequence, Strictly Increasing or Decreasing * Bernoulli’s Inequality * Bounded Sequence * Conv... nce * Theorem: A convergent sequence of real number has one and only one limit (i.e. limit of the se... equence * Theorem: A Cauchy sequence of real numbers is bounded. * Divergent Sequence * Theorem:... |>\frac{1}{2}s$. * Theorem: Let //a// and //b// be fixed real numbers if $\{s_n\}$ and $\{t_n\}$ con
Number Theory by Ms. Iqra Liaqat @msc:notes
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======Number Theory by Ms. Iqra Liaqat====== {{ :msc:notes:number-theory-iqra-liaqat.jpg?nolink|Number Theory by Ms. Iqra Liaqat}} Notes of number theory provided Ms. Iqra Liaqat is a very good addition
Topology: Short Questions and MCQs @msc:mcqs_short_questions
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hor of this page is Dr. [[:atiq]]. This page will be updated periodically. </callout> ===== Short qu... - Let $X=\{a\}$. Then what are the differences between discrete topology, indiscreet topology and confinite topology on $X$? - Let $X$ be a non-empty finite set. Then what is the difference between discrete and cofinite toplogy on $X$. - Le
Chapter 03 - Limits and Continuity @msc:real_analysis_notes_by_syed_gul_shah
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Theorem: Suppose (i) $(X,{d_x})$ and $(Y,{d_y})$ be two metric spaces (ii) $E\subset X$ (iii) $f:E\to... f(x)=l$ if and only if for every positive real number $\varepsilon$, there is $\delta>0$ such that $|f... f metric spaces) * Theorem: Let (i) //X, Y, Z// be metric spaces (ii) $E\subset X$ (iii) $f:E\to Y$,... // is continuous at //p//. * Theorem: Let //f// be defined on //X//. If //f// is continuous at $c\in
Syllabus for PU @msc:syllabus
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s no official links with PU. This information has been published for good cause.)) 2 years M.Sc Mathe... cs) Part-I and Part-II (Regular Scheme) are given below. <callout type="warning" icon="true" title="C... Regulations ===== The following regulations will be observed by M.Sc. (Mathematics) regular students ... art II. The topics of Viva Voce Examination shall be: * a) Analysis (Real, Complex and Functional)
Preparation Guide @msc:syllabus:uos
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ysics By Laldin Baig. Optional Subjects: ===1. Number Theory ( analytic number theory and algebraic number theory ) === * [[MSc:Notes:Number Theory by Anwar Khan]] ===2. Advance Group Theory === Books: *
Chapter 04 - Differentiation @msc:real_analysis_notes_by_syed_gul_shah
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* Derivative of a function * Theorem: Let //f// be defined on [//a//,//b//], if //f// is differentia... Examples * Local Maximum * Theorem: Let //f// be defined on [//a//,//b//], if //f// has a local ma... of vector valued function * Theorem: Let //f// be a continuous mapping of the interval [//a//,//b//... ] into a space $\mathbb{R}^k$ and $\underline{f}$ be differentiable in (//a//,//b//) then there exists
Normed Spaces: Short Questions and MCQs @msc:mcqs_short_questions
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esource.blogspot.com/2010/08/google-docs-viewer-embed-can-be-seen-in.html target=_blank>this page</a></b>."); } else { document.write(""); } //... c%2Fmcqs%2FShort_Questions_%20Normed_Spaces.pdf&embedded=true" width="600" height="780" style="border:
Targets @msc:notes
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d the notes for MSc or BS Mathematics, which will be published on MathCity.org. We are working hard to... --- // 2017/03/01 18:59// * **<del>Algebraic Number Theory</del>** Notes added with number theory. * **<del>Theory of relativity & analytic dynamics</
DOC Viewer @msc:notes
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/viewer|Google docs viewer]]. PDF of the file can be downloaded from this page. For other notes for MS