Merging man & maths https://www.mathcity.org/ Fri, 05 Jun 2026 14:36:49 +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/sp15-mth321/mcqs MCQs or Short Questions On this page, MCQs or short questions with out answers are given. Students 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$2n$$n \in \mathbb{Z}$$2\pi$$\pi$$\pi$$\sqrt{2}$$\sqrt{3}$$A$$f:A\to \mathbb{N}$$f$$f$$f$$A=\{x| x\in \mathbb{N} \wedge x^2 \leq 7 \}$$A$$\{s_n\}$$\lambda$$|s_n|<\lambda$$n\in\mathbb{Z}$$p$$|s_n|<p$$n\in\mathbb{Z}$$s$$|s_n|<s$$n… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:45:18 +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/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/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/math-103 MATH 103: Number Theory Objectives of the course This course shall assume no experience of background in number theory of theoretical mathematics. The course introduces various strategies for composing mathematical proofs. Course contents Number systems: natural numbers, integers, rational numbers, real numbers, complex numbers, the equivalence and the difference of cardinality between them, de Morvie’s theorem with application, hyperbolic ad logarithmic functions, introduction to number the… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:40:17 +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/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/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/sp14-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 16:40:29 +0000 https://www.mathcity.org/atiq/chem-501 CHEM-501: Basic Mathematics for Chemist Course contents Introdtuction; Review of basic algebra, Graphs and their significance in chemistry. Trigonometric, logarithmic and exponential functions. Differentiation, partial differentiation, differential equations and their use in chemical problems. Concept of maxima and minima. integration, Determinants and Matrices, their properties and use in chemical problems. solutions of linear equations (simple, determinant and matrices methods), operator the… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:40:04 +0000 https://www.mathcity.org/atiq/math-300 MATH-300: Basic Mathematics for Chemist Without mathematics the sciences cannot be understood, nor made clear, nor taught, nor learned. (Roger Bacon, 1214–1292) Course contents Introdtuction; Review of basic algebra, Graphs and their significance in chemistry. Trigonometric, logarithmic and exponential functions. Differentiation, partial differentiation, differential equations and their use in chemical problems. Concept of maxima and minima. integration, Determinants and Matrices, their prope… anonymous@undisclosed.example.com (Anonymous) Wed, 31 May 2023 05:38:37 +0000 https://www.mathcity.org/atiq/math-305 MATH-305: Real Analysis-I Objectives of the course: This is the first rigorous course in analysis and has a theoretical emphasis. It tegorously develops the fundamental ideas of calculus and is aimed to develop the students’ ability to deal with abstract mathematics and mathematical proofs. anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:40:21 +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/fa23-mth103 MTH103: Exploring Quantitative Skills Course Objectives This course aims to develop the basic mathematical skills which ultimately enhance problem-solving skills using inductive and deductive reasoning, Polya's strategy, and sets. The basic concepts will be develop with applications form the real world such as algebraic models with equations, rates, ratios, and percentages will be discussed. Students will also explore linear models, including rectangular coordinates, functions, empowering them… anonymous@undisclosed.example.com (Anonymous) Wed, 27 Sep 2023 13:47:12 +0000 https://www.mathcity.org/atiq/math-301 MATH-301: Complex Analysis Objectives of the course This is an introductory course in complex analysis, giving the basics of the theory along with applications, with an emphasis on applications of complex analysis and especially conformal mappings. Students should have a background in real analysis (as in the course Real Analysis I), including the ability to write a simple proof in an analysis context. $\cot 2z$ anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:40:18 +0000 https://www.mathcity.org/atiq/math-505 MATH-505: Complex Analysis Provisional Results MMAF13E101 = 65 MMAF13E102 = 65 MMAF13E103 = 58 MMAF13E104 = 58 MMAF13E105 = 78 MMAF13E106 = 62 MMAF13E107 = 50 MMAF13E108 = 75 MMAF13E109 = 61 MMAF13E110 = 50 MMAF13E111 = 50 MMAF13E112 = 85 $\cot 2z$ anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:40:23 +0000 https://www.mathcity.org/atiq/sp19-mth633 MTH633: Advanced Convex Analysis (Spring 2019) Convex sets, convex hull, their properties, separation theorems, hyperplane, Best approximation theorem and its applications, Farkas and Gordan Theorems, Extreme points and Polyhedral. Convex functions, Basic Definitions, properties, various generalizations, differentiable convex functions, subgradient, characterization and applications in linear and nonlinear optimization, complementarity problems and its equivalent formulations.$\mathbb{R}$$\math… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:40:40 +0000 https://www.mathcity.org/atiq/sp20-mth604 ~~DISCUSSION~~ MTH604: Fixed Point Theory and Applications (Spring 2020) Course Objectives: This course is intended as a brief introduction to the subject with a focus on Banach Fixed Point theorems fixed point theorem and its application to nonlinear differential equations, nonlinear integral equations, real and complex implicit functions theorems and system of nonlinear equations. Some generalizations and similar results e. g. Kannan Fixed Point theorems, Banach Fixed Point theorem for mul… anonymous@undisclosed.example.com (Anonymous) Sun, 07 Feb 2021 16:40:41 +0000