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- 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... Chapter 02** - A convergent sequence of real number has one and only one limit (i.e. limit of the se... }_{n}} \right\}$ and $\left\{ {{t}_{n}} \right\}$ be two convergent sequences such that $\underset{n\t... also converges to $s$. - For each irrational number $x$, there exists a sequence $\left\{ {{r}_{n}}
- 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 nor odd is * (A) 0 * (B) 2 * (C) $2n$ su... that $n \in \mathbb{Z}$ * (D) $2\pi$ - A number which is neither positive nor negative is *
- 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... ent. ===== Course contents ===== * The Real Number System: Ordered Fields. The Field of Reals. The Extended Real Number System. Euclidean Space. * Numerical Sequence... n the 18th century used the entire set of real numbers without having defined them cleanly. The first
- 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... ment. ===== Course contents ===== * The Real Number System: Ordered Fields. The Field of Reals. The Extended Real Number System. Euclidean Space. * Numerical Sequence... n the 18th century used the entire set of real numbers without having defined them cleanly. The first
- 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
- MTH321: Real Analysis I (Fall 2015)
- HTML><img src="http://mathcity.org/images/real_numbers.jpg" title="Number SYstem" class="mediaright" alt="Calculus" /></HTML> At the end of this course the students will be able to uunderstand the basic set theoretic state... elopment. ===== Course contents ===== The Real Number System: Ordered Fields. The Field of Reals. The
- MTH322: Real Analysis II (Spring 2023)
- ntiation, integration, sequences and series of numbers, that is many notions included in [[atiq:fa21-m... eq 1 \hbox{ and } x\in [a,b].$$ - Let $\{f_n\}$ be a sequence of functions, such that $\lim\limits_{... sts a convergent series $\sum M_n$ of positive numbers such that for all $x\in [a,b]$ $\left|f_n(x)\ri... _n \quad \hbox{for all}\,\, n.$ - Let $\{f_n\}$ be a sequence of functions defined on $[a,b]$. If $f
- 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 (Fall 2018)
- HTML><img src="http://mathcity.org/images/real_numbers.jpg" title="Number SYstem" class="mediaright" alt="Calculus" /></HTML> At the end of this course the students will be able to understand the basic set theoretic statem... ment. ===== Course contents ===== * The Real Number System: Ordered Fields. The Field of Reals. The
- MTH321: Real Analysis I (Fall 2019)
- ck}} At the end of this course the students will be able to understand the basic set theoretic statem... ment. ===== Course contents ===== * The Real Number System: Ordered Fields. The Field of Reals. The Extended Real Number System. Euclidean Space. * Numerical Sequence... n the 18th century used the entire set of real numbers without having defined them cleanly. The first
- MTH322: Real Analysis II (Fall 2021)
- ntiation, integration, sequences and series of numbers, that is many notion included in [[atiq:sp20-mt... infty }{{{x}^{-p}} dx}$, where $p$ is any real number. Discuss its convergence or divergence. - Supp... {f(x)g(x)dx}$ is convergent. - State and prove Abel's theorem for infinite integral. - If $f(x)$ i... fty }{\sin {{x}^{2}} dx}$ is convergent. - Use Abel's theorem to prove that $\int\limits_{0}^{\infty
- MTH321: Real Analysis I (Fall 2022)
- ox}} At the end of this course the students will be able to understand the basic set theoretic statem... ent. ===== Course contents ===== * The Real Number System: Ordered Fields. The Field of Reals. The Extended Real Number System. Euclidean Space. * Numerical Sequence... n the 18th century used the entire set of real numbers without having defined them cleanly. The first
- MTH321: Real Analysis 1
- HTML><img src="http://mathcity.org/images/real_numbers.jpg" title="Number SYstem" class="mediaright" alt="Calculus" /></HTML> At the end of this course the students will be able to uunderstand the basic set theoretic state... elopment. ===== Course contents ===== The Real Number System: Ordered Fields. The Field of Reals. The
- MTH321: Real Analysis 1 (Spring 2015)
- HTML><img src="http://mathcity.org/images/real_numbers.jpg" title="Number SYstem" class="mediaright" alt="Calculus" /></HTML> At the end of this course the students will be able to uunderstand the basic set theoretic state... elopment. ===== Course contents ===== The Real Number System: Ordered Fields. The Field of Reals. The
- MATH 103: Number Theory
- ====== MATH 103: Number Theory ====== ==== Objectives of the course ==== This course shall assume no experience of background in number theory of theoretical mathematics. The course in... athematical proofs. ==== Course contents ==== Number systems: natural numbers, integers, rational numbers, real numbers, complex numbers, the equivalence