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- MTH604: Fixed Point Theory and Applications (Spring 2020)
- valued mappings and related fixed point theorems. Best approximation theorems. =====Sample questions=... ove Banach contraction principle. - Let $(X,d)$ be a complete metric space and $T:X\to X$ be a mapping such that for some integer $m$, $T^m=\underbrace ... - State extreme value theorem. - Let $(X,d)$ be a compact metric space and $T:X\to X$ be a contra
- MTH604: Fixed Point Theory and Applications (Fall 2022)
- valued mappings and related fixed point theorems. Best approximation theorems. =====Sample questions=... ve Banach contraction principle. - Let $(X,d)$ be a metric space and $F:X\to X$ be a contration, then prove that $\{ F^n(x)\}$ is Cauchy sequence. - Let $(X,d)$ be a metric space and $F:X\to X$ be a contration, th
- MTH321: Real Analysis I (Spring 2023)
- ox}} At the end of this course the students will be able to understand the basic set theoretic statem... }_{n}} \right\}$ and $\left\{ {{t}_{n}} \right\}$ be two convergent sequences such that $\underset{n\t... f:[0,1]\to \mathbb{R}$ defined as $f(x)=\left\{ \begin{matrix} 0 \text{ if $x$ is rational,} \\ 1 \te... e f(b)$, then given a number $\lambda $ that lies between $f(a)$ and $f(b)$, there exist a point $c\in
- MCQs or Short Questions @atiq:sp15-mth321
- need to find the answer them self. This page will be updated occasionally and new MCQs or short question will be posted here. - A number which is neither even ... * (D) 7 - 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
- MTH322: Real Analysis II (Spring 2023)
- eq 1 \hbox{ and } x\in [a,b].$$ - Let $\{f_n\}$ be a sequence of functions, such that $\lim\limits_{... _n \quad \hbox{for all}\,\, n.$ - Let $\{f_n\}$ be a sequence of functions defined on $[a,b]$. If $f... ch function $f_n$ is continuous on $[a,b]$, then \begin{equation} \int_{a}^{b} f(x) dx = \lim\limits_{... /HTML> ====Resources for midterm ==== There will be two questions having three parts each. First part
- MTH321: Real Analysis I (Fall 2021)
- ox}} At the end of this course the students will be able to understand the basic set theoretic statem... otation, and insisted that there is no difference between rational and irrational numbers in this rega... d. </callout> =====Schedule===== The classes has been suspended due to COVID-19 pandemic. * Tuesday... ==== Please download PDF files of the notes given below. To view PDF files, there must be PDF Reader (
- MTH321: Real Analysis I (Spring 2020)
- ox}} At the end of this course the students will be able to understand the basic set theoretic statem... otation, and insisted that there is no difference between rational and irrational numbers in this rega... d. </callout> =====Schedule===== The classes has been suspended due to COVID-19 pandemic. * <del>Th... ==== Please download PDF files of the notes given below. To view PDF files, there must be PDF Reader (
- MATH-510: Topology
- ter round important 70%> Some questions are given below. These should be considered as sample and thousands of such questions can be created or constructed but if you understand the ... - Let $X=\{a\}$. Then what are the differences between discrete topology, indiscreet topology and c
- MTH321: Real Analysis I (Fall 2015)
- TML> At the end of this course the students will be able to uunderstand the basic set theoretic state... otation, and insisted that there is no difference between rational and irrational numbers in this rega... ase download PDF files of the notes handout given below. These files can be only viewed or print if there is PDF reader or viewer installed on your system
- MTH424: Convex Analysis (Fall 2020)
- ==== At the end of this course the students will be able to understand the concept of Convex Analysis... ities and their applications. Prepare students to be self independent and enhance their mathematical a... eir properties, Convex hull and their properties, Best approximation theorem. Convex functions, Basic ... ery convex function on closed interval is bounded below. * Prove that every convex function on close
- MTH480: Introductory Quantum Mechanics
- underlying physical principles. The relationship between classical and quantum mechanics is explored to illustrate how physical objects can be viewed both as a particle and a wave. ===== Cou... ==== Please download PDF files of the notes given below. To view PDF files, there must be PDF Reader (Viewer) installed on your PC or mobile or smartphone
- MTH251: Set Topology
- ===== At the end of this course the students will be able to understand the theory of metric spaces an... en in correct mathematical English. Students will be able to devise, organize and present brief soluti... their overall mathematical development. They will be improving such skills as mathematical writing and... the relative topology of $A=\{c,d\}$. * Let $A$ be a subset of topological space $X$. Then prove tha
- MTH322: Real Analysis II (Fall 2021)
- on an interval containing $0$. - Let $\{f_n\}$ be a sequence of functions, such that $\lim\limits_{... {2n}}{n^{p+1}(1+x^{2n})}, p>0.$ - Let $\{f_n\}$ be a sequence of functions defined on an interval $I... f$ is also continuous at $x_0$. - Let $\{f_n\}$ be a sequence of functions defined on an interval $I... $f$ is also continuous on $I$. - Let $\{f_n\}$ be a sequence of functions defined on $[a,b]$. If $f
- MTH103: Exploring Quantitative Skills
- lya's strategy, and sets. The basic concepts will be develop with applications form the real world suc... th equations, rates, ratios, and percentages will be discussed. Students will also explore linear mode... ==== Please download PDF files of the notes given below. To view PDF files, there must be PDF Reader (Viewer) installed on your PC or mobile or smartphone
- MTH321: Real Analysis I (Fall 2018)
- TML> At the end of this course the students will be able to understand the basic set theoretic statem... otation, and insisted that there is no difference between rational and irrational numbers in this rega... s=== Please download PDF files of the notes given below. To view PDF files, there must be PDF Reader (Viewer) installed on your PC or mobile or smartphone