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Real Analysis: Short Questions and MCQs @msc:mcqs_short_questions
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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 rational numbers coun
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 in t
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 ratio... property. * Field. * Proofs of axioms of real numbers. * Ordered field. * Theorems on ordered fiel... (a) Archimedean property (b) Between any two real numbers there exits a rational number. * Theorem: Given two real numbers //x// and //y//, $x<y$ there is an ir
Chapter 02 - Sequence and Series @msc:real_analysis_notes_by_syed_gul_shah
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quence * Theorem: A convergent sequence of real number has one and only one limit (i.e. limit of the seq... y Sequence * Theorem: A Cauchy sequence of real numbers is bounded. * Divergent Sequence * Theorem: ... $. * Theorem: Let //a// and //b// be fixed real numbers if $\{s_n\}$ and $\{t_n\}$ converge to //s// and... n$ and $t\ne 0$. * Theorem: For each irrational number //x//, there exists a sequence $\left\{{r_n}\righ
Preparation Guide @msc:syllabus:uos
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Physics By Laldin Baig. Optional Subjects: ===1. Number Theory ( analytic number theory and algebraic number theory ) === * [[MSc:Notes:Number Theory by Anwar Khan]] ===2. Advance Group Theory === Books: * Theo
Chapter 03 - Limits and Continuity @msc:real_analysis_notes_by_syed_gul_shah
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c}f(x)=l$ if and only if for every positive real number $\varepsilon$, there is $\delta>0$ such that $|f(... f// is continuous at $c\in X$ then there exists a number $\delta>0$ such that //f// is bounded on the open... n [//a//,//b//] and $f(a)\neq f(b)$, then given a number $\lambda$ that lies between $f(a)$ and $f(b)$, th
Targets @msc:notes
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d --- // 2017/03/01 18:59// * **<del>Algebraic Number Theory</del>** Notes added with number theory. * **<del>Theory of relativity & analytic dynamics</del>*
Syllabus for UoS (Private only) @msc:syllabus
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ule & regulation (M.A/M.Sc/M.Com) ===== - Total number of chances is three (1+2) in Part –I & four (1+3) in Part –II/ Composite Examination. - Minimum number of marks required to pass the examination are 40%
Syllabus for PU @msc:syllabus
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(iv) Rings and Modules * Paper IV-VI option (v) Number Theory * Paper IV-VI option (vi) Fluid Mechanic