This is beta site. https://beta.mathcity.org/ 2026-06-04T15:53:05+00:00 https://beta.mathcity.org/ https://beta.mathcity.org/_media/logo.png text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/cal2?rev=1737476034&do=diff MATH 102: Calculus II Course outline * Techniques of integration * Further applications of integration * Parametric equations and polar coordinates * Conic sections * Sequence and series * Power series representation of functions Assignments <div> <center> </div><div> </center> </div> text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/chem-501?rev=1737476034&do=diff 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… text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/fa14-mth321?rev=1737476034&do=diff MTH321: Real Analysis 1 <div><img src="http://mathcity.org/images/real_numbers.jpg" title="Number SYstem" class="mediaright" alt="Calculus" /></div> 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’ de… text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/fa14-mth424?rev=1737476034&do=diff MTH424: Convex Analysis Objectives: At the end of this course the students will be able to understand the concept of Convex Analysis, convex sets, convex functions, Differential of the convex function. Developing ability to study the Hadamard-Hermite inequalities and their applications. Prepare students to be self independent and enhance their mathematical ability by giving them home work and projects. text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/fa14-mth604?rev=1737476034&do=diff MTH604: Fixed Point Theory and Applications 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 multi-valued mappings are also ed… text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/fa15-mth321?rev=1737476034&do=diff MTH321: Real Analysis I (Fall 2015) <div><img src="http://mathcity.org/images/real_numbers.jpg" title="Number SYstem" class="mediaright" alt="Calculus" /></div> 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 th… text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/fa15-mth322?rev=1737476034&do=diff MTH322: Real Analysis II (Fall 2015) 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. text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/fa16-mth322?rev=1737476034&do=diff ~~DISCUSSION:off~~ MTH322: Real Analysis II (Fall 2016) <callout type=“info” icon=“true”> Do you have questions or comments? Please use Discussion at the end of this page. </callout> 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 text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/fa17-mth322?rev=1737476034&do=diff MTH322: Real Analysis II (Fall 2017) 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 text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/fa18-mth321?rev=1737476034&do=diff MTH321: Real Analysis I (Fall 2018) <div><img src="http://mathcity.org/images/real_numbers.jpg" title="Number SYstem" class="mediaright" alt="Calculus" /></div> 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… text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/fa18-mth322?rev=1737476034&do=diff 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 text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/fa19-mth321?rev=1737476034&do=diff 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… text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/fa19-mth322?rev=1737476034&do=diff 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 text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/fa19-mth611?rev=1737476034&do=diff MTH611: Integral Inequalities (Fall 2019) This course is offered to students of MS(Mathematics) at COMSATS University Islamabad. This is a three credit hour course. Contents Some Quadrature rules and their applications Ostrowski Inequality in L1-, Lp- and L∞ spaces and applications Grüss Inequality, its variants and applications Ostrowski- Grüss inequalities, their consequences and applications Purturbed results for Ostrowski and Ostrowski- Grüss type inequalities Inequalities for convex func… text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/fa20-mth211?rev=1737476034&do=diff 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… text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/fa20-mth322?rev=1737476034&do=diff MTH322: Real Analysis II (Fall 2020) 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 <div> <center> <div class="container-self"> <iframe class="responsive-iframe-self" src="https://www.youtube.com/embed/videoseries?list=PLNZrcn6oQNnen-xIz_5DjQbkwbQnu7Xgt" frameborder="0" allow="au… text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/fa20-mth424?rev=1737476034&do=diff MTH424: Convex Analysis (Fall 2020) [Convex Analysis] Objectives: At the end of this course the students will be able to understand the concept of Convex Analysis, convex sets, convex functions, Differential of the convex function. Developing ability to study the Hadamard-Hermite inequalities and their applications. Prepare students to be self independent and enhance their mathematical ability by giving them home work and projects.$f(x)=x$$\mathbb{R}$$f(x)=x^2$$\mathbb{R}$$f:[a,b]\to \mathbb{… text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/fa21-mth321?rev=1737476034&do=diff MTH321: Real Analysis I (Fall 2021) <callout type=“info” icon=“true”> Discussion is available at the end of this page. One is free to ask any question or comment. </callout> [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… text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/fa21-mth322?rev=1737476034&do=diff 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$… text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/fa22-mth321?rev=1737476034&do=diff 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… text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/fa22-mth604?rev=1737476034&do=diff ~~DISCUSSION~~ MTH604: Fixed Point Theory and Applications (Fall 2022) [FPTA] 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 f… text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/fa23-mth103?rev=1737476034&do=diff 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… text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/fa23-mth480?rev=1737476034&do=diff MTH480: Introductory Quantum Mechanics Objective The physical principles and mathematical formalism of quantum theory, with emphasis on applications to atomic, molecular, and many-body physics; scattering phenomena; and electromagnetism (photon physics). $x(t)={{t}^{3}}+2\sin t$$t=\dfrac{\pi }{6}$$v(t)={{t}^{2}}+t{{e}^{t}}$ text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/fa24-mth104?rev=1737476034&do=diff MTH104: Calculus & Analytical Geometry [MTH104: Calculus & Analytical Geometry] Course Objectives The main objective of Calculus and Analytical Geometry for students is to continue learning the basics of the calculus of functions of one variable. They will study functions, their types, limit and continuity of a function, derivatives, rate of change, chain rule, the concepts and techniques of integration, maxima and minima for the function of one variable, power series sequence and series, Tay… text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/fa24-mth731?rev=1737476034&do=diff MTH731: Topology [MTH731 Topology] Contents Introduction to Topological Structures and basic concepts (Revision) Topological Groups, Connected Spaces, Path Connected Spaces, Compact Spaces, Locally Connectedness and Locally Compactness, Homeomorphism and Topological Properties, n-spheres and Projective Spaces, The Separation axioms, Normal Spaces, The Urysohn Lemma, Numerability axioms, Covering spaces, The Tychnoff Theorem, Paracompact spaces, Manifolds (Brief Introduction), Imbedding of Man… text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/math-103?rev=1737476034&do=diff 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… text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/math-300?rev=1737476034&do=diff MATH-300: Basic Mathematics for Chemist <WRAP center round box 70%> Without mathematics the sciences cannot be understood, nor made clear, nor taught, nor learned. (Roger Bacon, 1214–1292) </WRAP> 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, De… text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/math-301?rev=1737476034&do=diff MATH-301: Complex Analysis <div> <img src="http://www.mathematicianspictures.com/Images/Eul_300w_post_us1.jpg" alt="image" title="image" class="mediaright" /><br> <center> </div> 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), includin… text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/math-305?rev=1737476034&do=diff 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. text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/math-505?rev=1737476034&do=diff MATH-505: Complex Analysis Provisional Results <WRAP third column> MMAF13E101 = 65 MMAF13E102 = 65 MMAF13E103 = 58 MMAF13E104 = 58 MMAF13E105 = 78 MMAF13E106 = 62 MMAF13E107 = 50 MMAF13E108 = 75 MMAF13E109 = 61 MMAF13E110 = 50 $\cot 2z$<div> <center> </div><div> </center> </div> text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/math-510-s2012?rev=1737476034&do=diff MATH-510: Topology <div> <img src="../images/Mug_and_Torus_morph.gif" alt="A continuous deformation (a type of homeomorphism) of a mug into a doughnut (torus) and back." title="Topologically equivalence figures" class="mediaright" /><br> <center> </div> 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 hom… text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/math-510?rev=1737476034&do=diff MATH-510: Topology <div> <img src="../images/Mug_and_Torus_morph.gif" alt="A continuous deformation (a type of homeomorphism) of a mug into a doughnut (torus) and back." title="Topologically equivalence figures" class="mediaright" /><br> </div> 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 (in… text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/math-608-s2012?rev=1737476034&do=diff MATH-608: Research Methodology <div> <img src="http://dl.dropbox.com/u/64787761/Research_Methodology.jpeg" alt="Book cover" title="Book cover" class="mediaright" /><br> <center> </div> 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. text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/math-608?rev=1737476034&do=diff MATH-608: History of Mathematics <div> <img src="https://dl.dropbox.com/u/64787761/Timeline_of_the_History_of_Mathematics.png" alt="Time line" title="Time line" class="mediaright" /><br> <center> </div> Course contents History of Numerations: Egyptian, Babylonian, Hindu and Arabic contributions. Algebra: Including the contributions of Al-Khwarzmi and Ibn Kura. Geometry: the areas, the work of Al-Toussi on Euclud’s axioms, Analysis. The Calculus: Newton, Leibniz and Gauss, The concept of limit… text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/math-731?rev=1737476034&do=diff MATH-731: Convex Analysis Convex functions on the real line, Continuity and differentiability of convex functions, Characterizations, Differences of convex functions, Conjugate convex functions, Convex sets and affine sets, Convex functions on a normed linear space, Continuity of convex functions on normed linear space, Differentiable convex function on normed linear space, The support of convex functions, Differentiability of convex function on normed linear space. text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/sp14-mth231?rev=1737476034&do=diff MTH231: Linear Algebra Introduction Linear algebra is the branch of mathematics deals with algebraic equations, spaces (vector and scalar), linear mappings between such spaces etc. Combined with the theory of calculus, linear algebra ensures to have methodologies to compute the solutions of system of equations (algebraic and differential). Techniques from linear algebra are also used in analytically geometry, engineering, physics, natural sciences and computer sciences and particularly in econ… text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/sp14-mth321?rev=1737476034&do=diff MTH321: Real Analysis 1 <div><img src="http://mathcity.org/images/real_numbers.jpg" title="Number SYstem" class="mediaright" alt="Calculus" /></div> 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’ de… text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/sp14-mth633?rev=1737476034&do=diff MTH633: Advanced Convex Analysis 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. text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/sp15-mth321?rev=1737476034&do=diff MTH321: Real Analysis 1 (Spring 2015) <div><img src="http://mathcity.org/images/real_numbers.jpg" title="Number SYstem" class="mediaright" alt="Calculus" /></div> 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 … text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/sp15-mth633?rev=1737476034&do=diff MTH633: Advanced Convex Analysis (Spring 2015) 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. text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/sp16-mth322?rev=1737476034&do=diff 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. text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/sp17-mth322?rev=1737476034&do=diff ~~DISCUSSION:closed~~ MTH322: Real Analysis II (Spring 2017) <callout type=“info” icon=“true”> Do you have questions or comments? Please use Discussion at the end of this page. </callout> 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 text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/sp17-mth633?rev=1737476034&do=diff MTH633: Advanced Convex Analysis (Spring 2017) 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. text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/sp18-mth251?rev=1737476034&do=diff MTH251: Set Topology [Set 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.$\mathbb{R}$$T_1$$\mathbb{Z}$$A=\{1,2,3,...,20\}$$\mathbb{R}$$\mathbb{Q}$$\mathbb{R}$$A=\left\{1,\frac{1}{2},\frac{1}{3},... \right\}$$A$$\mathbb{R}$$A=\mathbb{N}$$B=\{1,2,3,...,100\}$$C=… text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/sp18-mth604?rev=1737476034&do=diff MTH604: Fixed Point Theory and Applications Course Objectives: This course is intended as a brief introduction to the subject with a focus on Banach Fixed Point theorems fixed point theorem and its application to nonlinear differential equations, nonlinear integral equations, real and complex implicit functions theorems and system of nonlinear equations. Some generalizations and similar results e. g. Kannan Fixed Point theorems, Banach Fixed Point theorem for multi-valued mappings are also ed… text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/sp19-mth322?rev=1737476034&do=diff MTH322: Real Analysis II (Spring 2019) This course is offered to MSc, Semester II at Department of Mathematics, COMSATS University Islamabad, Attock campus. This course need rigorous knowledge of continuity, differentiation, integration, sequences and series of numbers, that is many notion included in text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/sp19-mth633?rev=1737476034&do=diff MTH633: Advanced Convex Analysis (Spring 2019) Convex sets, convex hull, their properties, separation theorems, hyperplane, Best approximation theorem and its applications, Farkas and Gordan Theorems, Extreme points and Polyhedral. Convex functions, Basic Definitions, properties, various generalizations, differentiable convex functions, subgradient, characterization and applications in linear and nonlinear optimization, complementarity problems and its equivalent formulations.$\mathbb{R}$$\math… text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/sp20-mth211?rev=1737476034&do=diff MTH211: Discrete Mathematics (Spring 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… text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/sp20-mth321?rev=1737476034&do=diff MTH321: Real Analysis I (Spring 2020) <callout type=“info” icon=“true”> Discussion is available at the end of this page. One is free to ask any question or comment. </callout> ~~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 vario… text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/sp20-mth604?rev=1737476034&do=diff ~~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… text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/sp21-mth211?rev=1737476034&do=diff 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… text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/sp21-mth604?rev=1737476034&do=diff ~~DISCUSSION~~ MTH604: Fixed Point Theory and Applications (Spring 2021) 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… text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/sp22-mth211?rev=1737476034&do=diff 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… text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/sp22-mth322?rev=1737476034&do=diff MTH322: Real Analysis II (Spring 2022) 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 notion included in <div> <center> <div class="container-self"> <iframe class="responsive-iframe-self" src="https://www.youtube.com/embed/videoseries?list=PLNZrcn6oQNnen-xIz_5DjQbkwbQnu7Xgt" frameborder="0" allow="a… text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/sp23-mth321?rev=1737476034&do=diff 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… text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/sp23-mth322?rev=1737476034&do=diff 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… text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/sp24-mth424?rev=1737476034&do=diff MTH424: Convex Analysis (Spring 2024) [Convex Analysis] Objectives: At the end of this course the students will be able to understand the concept of Convex Analysis, convex sets, convex functions, Differential of the convex function. Developing ability to study the Hadamard-Hermite inequalities and their applications. Prepare students to be self independent and enhance their mathematical ability by giving them home work and projects. text/html 2025-01-21T16:13:54+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/atiq/sp24-mth480?rev=1737476034&do=diff MTH480: Introductory Quantum Mechanics Objective The physical principles and mathematical formalism of quantum theory, with emphasis on applications to atomic, molecular, and many-body physics; scattering phenomena; and electromagnetism (photon physics).