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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 exists between any two real numbers. - Is the set of rati
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
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 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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c Sequence, Strictly Increasing or Decreasing * Bernoulli’s Inequality * Bounded Sequence * Conv... |>\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
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)
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... field. * Theorem: (a) Archimedean property (b) Between any two real numbers there exits a rational ... \sqrt{12}$ is irrational. * Question: Let //E// be a non-empty subset of an ordered set, suppose $\alpha$ is a lower bound of //E// and $\beta$ is an upper bound then prove that $\alpha\le \
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
Number Theory by Ms. Iqra Liaqat @msc:notes
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y==== In this section, the main heading are given below. <grid> <col sm="6"> * Well ordering princi... multiple * Greated common divisor * Relation between GCD and LCM * Linear Diophantine equation
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