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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 qu... e id="a3" collapsed="true">(D): Integers can only be even or odd but $2\pi$ is not an integer.</collap... se id="a6" collapsed="true">(C): Real numbers can be partitioned into rational and irrational. </colla... llapse> </panel><panel> 8. A set $A$ is said to be countable if there exists a function $f:A\to \mat
Syllabus for UoS (Private only) @msc:syllabus
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nd few optional subjects has been dropped. Please be alert --- // 2017/08/25 17:05// </WRAP> ===== E... hree courses are compulsory and the students will be required to choose three more courses from the li... P center round update 90%> The paper pattern will be as following. (updated for year 2013 and onward) ... he answer book having two marks each - 80% will be subjective. One have to attempt "four questions o
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 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... in //Y//. * Theorem: Let $f_1,f_2,f_3,...,f_k$ be real valued functions on a metric space //X// and
Chapter 02 - Sequence and Series @msc:real_analysis_notes_by_syed_gul_shah
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|>\frac{1}{2}s$. * Theorem: Let //a// and //b// be fixed real numbers if $\{s_n\}$ and $\{t_n\}$ con... \to \infty}{r_n}=x$. * Let a sequence $\{s_n\}$ be a bounded sequence. (i) If $\{s_n\}$ is monotonic... for all $n>m>n_0$. * Theorem: Let $\sum {a_n}$ be an infinite series of non-negative terms and let $\{s_n\}$ be a sequence of its partial sums then $\sum{a_n}$ i
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... pology and confinite topology on $X$? - Let $X$ be a non-empty finite set. Then what is the differen... crete and cofinite toplogy on $X$. - Let $\tau$ be a cofinite toplogy on $\mathbb{N}$. Then write an... e element of $\tau$. - Let $(\mathbb{Z}, \tau)$ be a cofinite topological spaces. * Is $\mathb
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
Syllabus for PU @msc:syllabus
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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)... M.Sc Part-I ===== The following five papers shall be studied in M.Sc. Part-I: - Paper I: Real Analys... ld papers of MSc Mathematics are given, which can be considered as old papers. * [[Papers:Old papers
Chapter 01 - Real Number System @msc:real_analysis_notes_by_syed_gul_shah
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l //p// such that $p^2=2$. * Theorem: Let //A// be the set of all positive rationals //p// such that... \sqrt{12}$ is irrational. * Question: Let //E// be a non-empty subset of an ordered set, suppose $\a
Preparation Guide @msc:syllabus:uos
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hematical statistic) Note: optional subjects can be chosen other then mentioned above and 100 marks viva will be conducted at the end of part-2 examination from p
Normed Spaces: Short Questions and MCQs @msc:mcqs_short_questions
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blogspot.com/2010/08/google-docs-viewer-embed-can-be-seen-in.html target=_blank>this page</a></b>.");
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
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