Merging man & maths https://www.mathcity.org/ Wed, 03 Jun 2026 23:45:08 +0000 FeedCreator 1.8 https://www.mathcity.org/_media/logo.svg https://www.mathcity.org/ https://www.mathcity.org/atiq/sp23-mth321 MTH321: Real Analysis I (Spring 2023) ~~DISCUSSION~~ [Photo-illustration of Zeno's Paradox] At the end of this course the students will be able to understand the basic set theoretic statements and emphasize the proofs’ development of various statements by induction. Define the limit of, a function at a value, a sequence and the Cauchy criterion. Prove various theorems about limits of sequences and functions and emphasize the proofs’ development. Define continuity of a function and uniform con… anonymous@undisclosed.example.com (Anonymous) Wed, 14 Jun 2023 14:47:57 +0000 https://www.mathcity.org/atiq/fa21-mth321 MTH321: Real Analysis I (Fall 2021) Discussion is available at the end of this page. One is free to ask any question or comment. [Photo-illustration of Zeno's Paradox] At the end of this course the students will be able to understand the basic set theoretic statements and emphasize the proofs’ development of various statements by induction. Define the limit of, a function at a value, a sequence and the Cauchy criterion. Prove various theorems about limits of sequences and functions and emphas… anonymous@undisclosed.example.com (Anonymous) Fri, 28 Oct 2022 11:10:02 +0000 https://www.mathcity.org/atiq/sp20-mth321 MTH321: Real Analysis I (Spring 2020) Discussion is available at the end of this page. One is free to ask any question or comment. ~~DISCUSSION~~ [Photo-illustration of Zeno's Paradox] At the end of this course the students will be able to understand the basic set theoretic statements and emphasize the proofs’ development of various statements by induction. Define the limit of, a function at a value, a sequence and the Cauchy criterion. Prove various theorems about limits of sequences and fun… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:40:41 +0000 https://www.mathcity.org/atiq/fa14-mth321 MTH321: Real Analysis 1 At the end of this course the students will be able to uunderstand the basic set theoretic statements and emphasize the proofs’ development of various statements by induction. Define the limit of, a function at a value, a sequence and the Cauchy criterion. Prove various theorems about limits of sequences and functions and emphasize the proofs’ development. Define continuity of a function and uniform continuity of a function, prove various theorems about continuous func… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:40:06 +0000 https://www.mathcity.org/atiq/fa19-mth321 MTH321: Real Analysis I (Fall 2019) [Photo-illustration of Zeno's Paradox by Juliana Jiménez Jaramillo. Photo by Twildlife/Thinkstock] At the end of this course the students will be able to understand the basic set theoretic statements and emphasize the proofs’ development of various statements by induction. Define the limit of, a function at a value, a sequence and the Cauchy criterion. Prove various theorems about limits of sequences and functions and emphasize the proofs’ development. Def… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:40:11 +0000 https://www.mathcity.org/atiq/sp15-mth321 MTH321: Real Analysis 1 (Spring 2015) At the end of this course the students will be able to uunderstand the basic set theoretic statements and emphasize the proofs’ development of various statements by induction. Define the limit of, a function at a value, a sequence and the Cauchy criterion. Prove various theorems about limits of sequences and functions and emphasize the proofs’ development. Define continuity of a function and uniform continuity of a function, prove various theorems about c… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:40:32 +0000 https://www.mathcity.org/atiq/sp16-mth322 MTH322: Real Analysis II (Spring 2016) This course was teach to MSc III and IV. Course Contents: Sequences of functions: convergence, uniform convergence, uniform convergence and continuity, uniform convergence and integration, uniform convergence and differentiation, the exponential and logarithmic function, the trigonometric functions. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:40:34 +0000 https://www.mathcity.org/atiq/fa15-mth321 MTH321: Real Analysis I (Fall 2015) At the end of this course the students will be able to uunderstand the basic set theoretic statements and emphasize the proofs’ development of various statements by induction. Define the limit of, a function at a value, a sequence and the Cauchy criterion. Prove various theorems about limits of sequences and functions and emphasize the proofs’ development. Define continuity of a function and uniform continuity of a function, prove various theorems about con… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:40:08 +0000 https://www.mathcity.org/atiq/fa16-mth322 ~~DISCUSSION:off~~ MTH322: Real Analysis II (Fall 2016) Do you have questions or comments? Please use Discussion at the end of this page. This course is offered to MSc, Semester III at Department of Mathematics, COMSATS Institute of Information Technology, Attock campus. The is course need rigorous knowledge of continuity, differentiation, integration, sequences and series of numbers, that is many notion included in anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:40:09 +0000 https://www.mathcity.org/atiq/fa18-mth321 MTH321: Real Analysis I (Fall 2018) At the end of this course the students will be able to understand the basic set theoretic statements and emphasize the proofs’ development of various statements by induction. Define the limit of, a function at a value, a sequence and the Cauchy criterion. Prove various theorems about limits of sequences and functions and emphasize the proofs’ development. Define continuity of a function and uniform continuity of a function, prove various theorems about cont… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:40:10 +0000 https://www.mathcity.org/atiq/fa22-mth321 MTH321: Real Analysis I (Fall 2022) ~~DISCUSSION~~ [Photo-illustration of Zeno's Paradox] At the end of this course the students will be able to understand the basic set theoretic statements and emphasize the proofs’ development of various statements by induction. Define the limit of, a function at a value, a sequence and the Cauchy criterion. Prove various theorems about limits of sequences and functions and emphasize the proofs’ development. Define continuity of a function and uniform conti… anonymous@undisclosed.example.com (Anonymous) Mon, 15 May 2023 07:16:43 +0000 https://www.mathcity.org/atiq/sp23-mth322 MTH322: Real Analysis II (Spring 2023) [MTH322: Real Analysis II (Spring 2023)] This course is offered to BS, Semester VI at Department of Mathematics, COMSATS University Islamabad, Attock campus. This course need rigorous knowledge of continuity, differentiation, integration, sequences and series of numbers, that is many notions included in $f\in \mathcal{R}[a,b]$$b\ge a$$f(x)\ge 0$$x\ge a$$\int_{\,a}^{\,\infty }{f(x)\,dx}$$M>0$$\int\limits_{a}^{b}{f(x)\,dx}\leq M$$b\ge a$$f(x)$$g(x)$$x>a$$\li… anonymous@undisclosed.example.com (Anonymous) Thu, 15 Jun 2023 01:08:47 +0000 https://www.mathcity.org/atiq/fa21-mth322 MTH322: Real Analysis II (Fall 2021) This course is offered to MSc, Semester II at Department of Mathematics, COMSATS University Islamabad, Attock campus. This course need rigorous knowledge of continuity, differentiation, integration, sequences and series of numbers, that is many notion included in $\int_{1}^{\infty }{{{x}^{-p}} dx}$$p$$f\in \mathcal{R}[a,b]$$b\ge a$$f(x)\ge 0$$x\ge a$$\int_{a}^{\infty }{f(x) dx}$$M>0$$\int\limits_{a}^{b}{f(x)\,dx} \le M$$b\ge a$$f\in \mathcal{R}[a,b]$$b\ge a$… anonymous@undisclosed.example.com (Anonymous) Thu, 30 Dec 2021 19:16:17 +0000 https://www.mathcity.org/atiq/fa18-mth322 MTH322: Real Analysis II (Fall 2018) This course is offered to MSc, Semester II at Department of Mathematics, COMSATS University Islamabad, Attock campus. This course need rigorous knowledge of continuity, differentiation, integration, sequences and series of numbers, that is many notion included in anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:40:11 +0000 https://www.mathcity.org/atiq/fa20-mth211 MTH211: Discrete Mathematics (Fall 2020) Course Objectives: Discrete Mathematics is branch of Mathematics which deals with discrete structures like logic. sequences, graphs, relations in contrast to Calculus. where we enjoy the continuity of functions and the set of real numbers. This course is introduction to discrete structures which are not the part of main stream courses. Discrete Mathematics has applications in Computer Science. Economics and Decision Making etc. This course will help t… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:40:14 +0000 https://www.mathcity.org/atiq/sp17-mth322 ~~DISCUSSION:closed~~ MTH322: Real Analysis II (Spring 2017) Do you have questions or comments? Please use Discussion at the end of this page. This course is offered to MSc, Semester III at Department of Mathematics, COMSATS Institute of Information Technology, Attock campus. The is course need rigorous knowledge of continuity, differentiation, integration, sequences and series of numbers, that is many notion included in anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:40:35 +0000 https://www.mathcity.org/atiq/sp21-mth211 MTH211: Discrete Mathematics (Fall 2020) Course Objectives: Discrete Mathematics is branch of Mathematics which deals with discrete structures like logic. sequences, graphs, relations in contrast to Calculus. where we enjoy the continuity of functions and the set of real numbers. This course is introduction to discrete structures which are not the part of main stream courses. Discrete Mathematics has applications in Computer Science. Economics and Decision Making etc. This course will help t… anonymous@undisclosed.example.com (Anonymous) Thu, 10 Jun 2021 09:02:12 +0000 https://www.mathcity.org/atiq/sp22-mth211 MTH211: Discrete Mathematics (Spring 2022) Course Objectives: Discrete Mathematics is branch of Mathematics which deals with discrete structures like logic. sequences, graphs, relations in contrast to Calculus. where we enjoy the continuity of functions and the set of real numbers. This course is introduction to discrete structures which are not the part of main stream courses. Discrete Mathematics has applications in Computer Science. Economics and Decision Making etc. This course will help… anonymous@undisclosed.example.com (Anonymous) Mon, 12 Sep 2022 04:56:59 +0000 https://www.mathcity.org/atiq/fa19-mth322 MTH322: Real Analysis II (Fall 2019) This course is offered to MSc, Semester II at Department of Mathematics, COMSATS University Islamabad, Attock campus. This course need rigorous knowledge of continuity, differentiation, integration, sequences and series of numbers. these notions included in anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:40:12 +0000 https://www.mathcity.org/atiq/math-510 MATH-510: Topology Topology is an important branch of mathematics that studies all the “qualitative” or “discrete” properties of continuous objects such as manifolds, i.e. all the properties that aren't changed by any continuous transformations except for the singular (infinitely extreme) ones.$(T_0, T_1, T_2)$$\mathbb{R}$$X=\{a\}$$X$$X$$X$$\tau$$\mathbb{N}$$\tau$$(\mathbb{Z}, \tau)$$\mathbb{N}$$\tau$$A=\{\pm 100,\pm 101, \pm 102, ... \}$$\tau$$E=\{0,\pm 2,\pm 4,...\}$$\tau$$\tau$$B=\{1,2,3,...… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:40:25 +0000 https://www.mathcity.org/atiq/math-510-s2012 MATH-510: Topology Objectives of the course This is an introductory course in topology, giving the basics of the theory. Course contents Topological spaces, bases and sub-bases, first and second axiom of countability, separability, continuous functions and homeomorphism, finite product space. Separation axioms $(T_0, T_1, T_2)$ anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:40:24 +0000 https://www.mathcity.org/atiq/math-608-s2012 MATH-608: Research Methodology Objectives of the course Introduction to the students will be given that research in mathematics is conducted covering every fact of the research process, finding and defending suitable problems, performing literature survey. anonymous@undisclosed.example.com (Anonymous) Wed, 29 Sep 2021 16:16:53 +0000