MathCity.org

MATH-510: Topology

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:40:25 +0000

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,...…

MATH-510: Topology

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:40:24 +0000

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 $(T_0, T_1, T_2)$

Preparation Guide

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 17:00:44 +0000

Preparation Guide This guide is made by Mr. Anwar Khan, PhD. We are very thankful to him for sharing. This guide is helpful to prepare papers for MSc Mathematics (annual system) from University of Sargodha. Part 1 1. REAL ANAYSIS * Real Analysis (Notes by Syed Gul Shah) * Chapter # 08 sequences and series of Mathematical Method by SM Yousaf (solutions are available $z= f(x,y)$

MTH251: Set Topology (Spring 25)

anonymous@undisclosed.example.com (Anonymous) — Sun, 01 Feb 2026 14:28:11 +0000

MTH251: Set Topology (Spring 25) [MTH251 Set Topology] Set topology is a branch of mathematics that studies the properties of shapes and spaces that remain unchanged even if they are stretched, twisted, or deformed (without tearing or gluing). It helps us understand concepts like continuity, connectedness, and boundaries.$\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,.…

MTH251: Set Topology (Spring 18)

anonymous@undisclosed.example.com (Anonymous) — Fri, 07 Feb 2025 11:25:49 +0000

MTH251: Set Topology (Spring 18) [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,.…

MTH251: Set Topology (Spring 25)

anonymous@undisclosed.example.com (Anonymous) — Tue, 29 Apr 2025 10:10:47 +0000

MTH424: Convex Analysis (Spring 2025)

anonymous@undisclosed.example.com (Anonymous) — Mon, 16 Jun 2025 18:51:28 +0000

MTH424: Convex Analysis (Spring 2025) [Convex Analysis] Convex analysis is a branch of mathematics that studies convex sets and convex functions. A set is convex if a straight line between any two points in the set always stays inside it. This field is important in optimization, economics, and engineering. It helps in solving real-world problems like minimizing costs, maximizing profits, and designing efficient systems. Convex analysis is widely used in machine learning, finance, and physics. 😊…

MTH424: Convex Analysis

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:40:06 +0000

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.

MTH322: Real Analysis II (Fall 2016)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:40:09 +0000

~~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

MTH322: Real Analysis II (Fall 2017)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:40:10 +0000

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

MTH322: Real Analysis II (Fall 2018)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:40:11 +0000

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

MTH322: Real Analysis II (Fall 2019)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:40:12 +0000

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

MTH322: Real Analysis II (Fall 2020)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:40:14 +0000

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

MTH424: Convex Analysis (Fall 2020)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:40:16 +0000

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{…

MTH322: Real Analysis II (Fall 2021)

anonymous@undisclosed.example.com (Anonymous) — Thu, 30 Dec 2021 19:16:17 +0000

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$…

MATH-300: Basic Mathematics for Chemist

anonymous@undisclosed.example.com (Anonymous) — Wed, 31 May 2023 05:38:37 +0000

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…

MATH-301: Complex Analysis

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:40:18 +0000

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. $\cot 2z$

MTH231: Linear Algebra

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:40:27 +0000

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…

MTH322: Real Analysis II (Spring 2017)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:40:35 +0000

~~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

MTH633: Advanced Convex Analysis (Spring 2017)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:40:36 +0000

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.

MTH322: Real Analysis II (Spring 2019)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:40:39 +0000

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

MTH633: Advanced Convex Analysis (Spring 2019)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:40:40 +0000

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…

MTH322: Real Analysis II (Spring 2022)

anonymous@undisclosed.example.com (Anonymous) — Wed, 13 Apr 2022 05:45:43 +0000

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

MTH322: Real Analysis II (Spring 2023)

anonymous@undisclosed.example.com (Anonymous) — Thu, 15 Jun 2023 01:08:47 +0000

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…

MTH424: Convex Analysis (Spring 2024)

anonymous@undisclosed.example.com (Anonymous) — Fri, 29 Mar 2024 03:48:00 +0000

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.

Applied Mathematics (Paper A & B)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:55:46 +0000

Applied Mathematics (Paper A & B) This paper consista of two papers of 100 marks each. One paper is called “Paper A” and other is called “Paper B”. Paper A * NOTE: attempt two questions from each section. SECTION-I (4/12: 17,17,17,17) $(\lambda ,\mu )$

B-Course of Mathematics (Paper A & B)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:55:55 +0000

B-Course of Mathematics (Paper A & B) This subject is consists of two papers of 100 marks each. One is called “Paper A” and other is called “Paper B”. This page is updated on February 15, 2015. This syllabus is for 1st Annual 2015 and onward organized by University of Sargodha, Sargodha.$(\lambda ,\mu )$

Question 14 and 15, Exercise 6.2

anonymous@undisclosed.example.com (Anonymous) — Sat, 08 Mar 2025 08:59:57 +0000

Question 14 and 15, Exercise 6.2 Solutions of Question 14 and 15 of Exercise 6.2 of Unit 06: Permutation and Combination. This is unit of Model Textbook of Mathematics for Class XI published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan. $3$$=7$$=3$$={ }^{7} P_{3}=\dfrac{7!}{4!}=210$$5$$3$$2$$3$$=31=6$$=(5!\times 3!\times 2!) \times 31=8640$

ADS/BSc

anonymous@undisclosed.example.com (Anonymous) — Sat, 13 Jan 2024 11:00:49 +0000

ADS/BSc One this page we have listed notes/resources widely used in BSc or in Associated Degree of Science (ADS). This includes notes of some famous books and other resources. Notes of Famous Books Notes of Calculus with Analytic Geometry Notes of Calculus with Analytic Geometry Notes of Mathematical Method Notes of Mathematical Method Introduction to Mechanics Introduction to Mechanics Other notes Notes of Mechanics Notes of Mechanics written by different authors for BSc or BS…

Khuram Ali Khan

anonymous@undisclosed.example.com (Anonymous) — Fri, 13 Jun 2025 12:03:59 +0000

Khuram Ali Khan Khuram Ali Khan, PhD Associate Professor Department of Mathematics University of Sargodha Sargodha - PAKISTAN. Email: Field of Research: Difference and functional equations, Real functions, Mathematical inequalities involving convex functions, Time Scales Calculus, Soft Sets

PPSC General Information, Syllabus, Paper Pattern

anonymous@undisclosed.example.com (Anonymous) — Sun, 24 May 2026 17:45:57 +0000

~~DISCUSSION~~ PPSC General Information, Syllabus, Paper Pattern [PPSC] Our aim is to give general information, syllabus and paper pattern of paper couducted by Punjab Public Service Commission (PPSC) for the post of Lecturer in Mathematics. This page might be helpful for other jobs as subject specialist or for public service commission of other provinces.

MATH-731: Convex Analysis

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:40:27 +0000

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.

Notes of Calculus with Analytic Geometry

anonymous@undisclosed.example.com (Anonymous) — Mon, 30 May 2022 17:44:37 +0000

Notes of Calculus with Analytic Geometry [Calculus with Analytic Geometry by Dr. S. M. Yusuf and Prof. Muhammad Amin] Calculus with Analytic Geometry by Dr. S. M. Yusuf and Prof. Muhammad Amin, published by Ilmi Kitab Khana, Lahore-Pakistan is one of the books studied widely in Bachelor and undergraduate classes inclduing different engineering programs. There are total of ten chapters. Solutions of the books are given in the chapters listed below. The only aim to publish the soltuions is to pro…

Notes of Mathematical Method

anonymous@undisclosed.example.com (Anonymous) — Sun, 02 Jul 2023 07:49:56 +0000

Notes of Mathematical Method [BSc Mathematical Method] Notes of the Mathematical Method written by by S.M. Yusuf, A. Majeed and M. Amin and published by Ilmi Kitab Khana, Lahore. This is an old and good book of mathematical method. The notes given here are provided by awesome peoples, who dare to help others. Some of the notes are send by the authors of these notes and other are send by people who didn't write but share these notes as Open Educational Resources (OER). We are thankful to

Syllabus for UoS (Private only)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:50:15 +0000

Syllabus for UoS (Private only) Syllabus and scheme of studies for private students doing MSc Mathematics from University of Sargodha, Sargodha. The syllabus has been changed and few optional subjects has been dropped. Please be alert --- 2017/08/25 17:05

General Mathematics (Paper A & B)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:55:55 +0000

General Mathematics (Paper A & B) This subject is consists of two papers of 100 marks each. One is called “Paper A” and other is called “Paper B”. This syllabus is for 1st Annual 2015 and onward organized by University of Sargodha (UoS), Sargodha.

Exercise 6.2 (Solutions)

anonymous@undisclosed.example.com (Anonymous) — Sat, 08 Mar 2025 08:59:59 +0000

Exercise 6.2 (Solutions) The solutions of the Exercise 6.1 of book “Model Textbook of Mathematics for Class XI” published by National Book Foundation (NBF) as Federal Textbook Board, Islamabad, Pakistan are given on this page. This exercise consists of the question related to factorial function.$n!$$$ n!=\left\{\begin{array}{l} n(n-1)(n-2)\cdot \ldots \cdot 3 \cdot 2 \cdot 1 \text{ if } n\geq 1,\\ 1 \text{ if } n=0. \end{array} \right. $$$n \in \mathbb{N}$${ }^n P_r=\frac{n!}{(n-r)!}$$\quad{ }^…

FSc/ICS Part 1 (Mathematics): PTB

anonymous@undisclosed.example.com (Anonymous) — Sat, 19 Jul 2025 17:19:20 +0000

FSc/ICS Part 1 (Mathematics): PTB This is an old book. Notes of new book are available at following URL: [Textbook of Algebra and Trigonometry Class XI] Textbook of Algebra and Trigonometry Class XI is published by Punjab Textbook Board (PTB) Lahore, Pakistan. The book has total of 14 chapters.

Home

anonymous@undisclosed.example.com (Anonymous) — Tue, 24 Mar 2026 18:10:06 +0000

Home Welcome to MathCity.org. Please browse the website by using navigation bar or search the website. More Quotes :---: MathCity.org Updates * | FSc (PECTAA) | Solutions of the many exercises of Mathematics 11 (by PECTAA) has been add. read more for download NEW * | Notes | Mechanics III (Analytic Dynamics II) by Dr Babar Ahmad has been added in the notes section.

Notes of Mathematics

anonymous@undisclosed.example.com (Anonymous) — Mon, 25 May 2026 18:19:50 +0000

Notes of Mathematics [Notes of Mathematics] Mathematics is a language of science and is a basic need for physical or natural sciences as well as social sciences. On this page, notes on different subjects related to mathematics are listed. These notes or resources might be helpful for ADS or BS or MSc or MPhil Mathematics. These notes are send by different students or teachers. We are very thankful to them for sending us these notes. These notes are provided as it is as open educational resource…

Open Notes

anonymous@undisclosed.example.com (Anonymous) — Sat, 28 Jun 2025 19:08:38 +0000

Open Notes What are Open Notes? [Open Notes on Mathematics] We're planning to release notes and books related to mathematics. We'll give readers and teachers the original files. This way, they can update the materials to fit their own needs. We call these resources “Open Notes

CHEM-501: Basic Mathematics for Chemist

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:40:04 +0000

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…

MTH604: Fixed Point Theory and Applications

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:40:08 +0000

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…

MTH322: Real Analysis II (Fall 2015)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:40:09 +0000

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.

MTH611: Integral Inequalities (Fall 2019)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:40:12 +0000

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…

MTH604: Fixed Point Theory and Applications (Fall 2022)

anonymous@undisclosed.example.com (Anonymous) — Fri, 06 Jan 2023 04:37:11 +0000

~~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…

MTH103: Exploring Quantitative Skills

anonymous@undisclosed.example.com (Anonymous) — Wed, 27 Sep 2023 13:47:12 +0000

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…

MTH480: Introductory Quantum Mechanics

anonymous@undisclosed.example.com (Anonymous) — Sat, 07 Oct 2023 18:27:32 +0000

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}}$

MTH104: Calculus & Analytical Geometry

anonymous@undisclosed.example.com (Anonymous) — Wed, 25 Dec 2024 17:21:25 +0000

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…

MTH731: Topology

anonymous@undisclosed.example.com (Anonymous) — Wed, 25 Dec 2024 18:38:41 +0000

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…

CSC456: Stochastic Processes (Fall 2025)

anonymous@undisclosed.example.com (Anonymous) — Sun, 28 Dec 2025 14:20:45 +0000

CSC456: Stochastic Processes (Fall 2025) [Stochastic Processes (Fall 2025), Image Courtesy: Gemini] Course Objectives: * To define basic concepts from the theory of Markov chains and present proofs for the most important theorems. * To compute probabilities of transition between states and return to the initial state after long time intervals in Markov chains.

MTH324: Complex Analysis (Fall 2025)

anonymous@undisclosed.example.com (Anonymous) — Sun, 28 Sep 2025 07:23:19 +0000

MTH324: Complex Analysis (Fall 2025) [MTH324: Complex Analysis (Fall 2025) Courtesy: Copilot] Course Objectives: At the end of this course the students will be able to understand the basic properties of functions of a complex variable with the theory of analytic functions and its applications. Course contents:

MATH 103: Number Theory

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:40:17 +0000

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…

MATH-305: Real Analysis-I

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:40:21 +0000

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.

MATH-505: Complex Analysis

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:40:23 +0000

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 $\cot 2z$

MTH633: Advanced Convex Analysis

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:40:31 +0000

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.

MTH633: Advanced Convex Analysis (Spring 2015)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:40:33 +0000

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.

MTH322: Real Analysis II (Spring 2016)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:40:34 +0000

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.

MTH604: Fixed Point Theory and Applications

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:40:39 +0000

MTH604: Fixed Point Theory and Applications (Spring 2020)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:40:41 +0000

~~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…

MTH604: Fixed Point Theory and Applications (Spring 2021)

anonymous@undisclosed.example.com (Anonymous) — Mon, 22 Feb 2021 15:12:31 +0000

~~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…

MTH480: Introductory Quantum Mechanics

anonymous@undisclosed.example.com (Anonymous) — Wed, 14 Feb 2024 09:26:16 +0000

CSC456: Stochastic Processes (Spring 2026)

anonymous@undisclosed.example.com (Anonymous) — Wed, 03 Jun 2026 08:38:47 +0000

CSC456: Stochastic Processes (Spring 2026) [Stochastic Processes (Spring 2026), Image Courtesy: Gemini] Course Learning Outcomes: * To define basic concepts from the theory of Markov chains and present proofs for the most important theorems. * To compute probabilities of transition between states and return to the initial state after long time intervals in Markov chains.

Notes of Vector Analysis

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:40:54 +0000

Notes of Vector Analysis [Vector Ananlysis] Notes of the vector analysis are given on this page. These notes are helpful for BSc or equivalent classes. These notes are written by Amir Taimur Mohmand of University of Peshawar. The books of these notes is not known. If you know about the book, please inform us.$f$$P$

Syllabus for M.Sc Mathematics

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:43:47 +0000

Syllabus for M.Sc Mathematics Syllabus for PU Scheme of studies and syllabus for M.Sc Mathematics for University of the Punjab. Syllabus for UoS (Private only) Scheme of studies and syllabus for M.Sc Mathematics for University of Sargodha. * Preparation Guide UPD * Read about suggestion given by Mr. Anwar Khan for notes, books and preparation.

Elementary Linear Algebra by Muhammad Usman Hamid

anonymous@undisclosed.example.com (Anonymous) — Sun, 10 Dec 2023 14:05:12 +0000

Elementary Linear Algebra by Muhammad Usman Hamid [Elementary Linear Algebra by Muhammad Usman Hamid] Linear Algebra is the study of vectors and linear transformations. The main objective of this course is to help students learn in rigorous manner, the tools and methods essential for studying the solution spaces of problems in mathematics, engineering, the natural sciences and social sciences and develop mathematical skills needed to apply these to the problems arising within their field of st…

Fluid Dynamics I by Muhammad Usman Hamid

anonymous@undisclosed.example.com (Anonymous) — Sun, 03 May 2026 08:26:32 +0000

Fluid Dynamics I by Muhammad Usman Hamid [Fluid Dynamics I by Muhammad Usman Hamid] Explore comprehensive notes on Fluid Dynamics by Muhammad Usman Hamid. Covers fundamental concepts (viscosity, stress fields, continuum), fluid statics, and differential analysis. Special thanks to Mr. Anwar Khan for contributing these resources to MathCity.org.

History of Mathematics by Muhammad Usman Hamid

anonymous@undisclosed.example.com (Anonymous) — Tue, 08 Aug 2023 12:01:51 +0000

History of Mathematics by Muhammad Usman Hamid [History of Mathematics by Muhammad Usman Hamid] Mathematics is a unique aspect of human thought, and its history differs in essence from all other histories. These notes are written by Muhammad Usman Hamid. We are very thankful to him for sharing these notes on our website.

Mechanics III (Analytic Dynamics II) by Dr Babar Ahmad

anonymous@undisclosed.example.com (Anonymous) — Sat, 10 May 2025 17:33:01 +0000

Mechanics III (Analytic Dynamics II) by Dr Babar Ahmad [Mechanics III (Analytic Dynamics II) by Dr Babar Ahmad] We are very thankful to Dr Babar Ahmad for sharing his book on MathCity.org. This book is very helpful for undergraduate students of Science and Engineering Programs. This book is shared by the permission of the author and he keeps the copyright of the book.

Muzammil Tanveer

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:44:45 +0000

Muzammil Tanveer We are very thankful to Mr. Muzammil Tanveer for his contribution to the website. Mr. Muzammil Tanveer is also an expert to compose mathematics notes, books or papers. You may contact him via his email or cell number given below for professional paid composing.

Quotes for the May

anonymous@undisclosed.example.com (Anonymous) — Fri, 28 Apr 2023 18:45:11 +0000

Quotes for the May مختصراً، پوری دنیا خلا اور وقت میں اشیا کی ریاضیاتی طور پر ظاہر کی جانے والی حرکات کا مجموعہ ہے، اور پوری کائنات ایک عظیم، ہم آہنگ اور ریاضیاتی طور پر تیار کی گئی مشین ہے۔۔۔

How to prepare admission test (A short guide)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:50:25 +0000

How to prepare admission test (A short guide) MathCity.org does not represent any official or government/semi-government/private educational institute or board or university. The resources given on the site holds no official position in government/semi-government/private educational institute or board or university. While using a resources given on this site you agreed to the term that we (MathCity.org or person related to MathCity.org) do not take any responsibility for these resources. The sug…

A-Course of Mathematics (Paper A & B)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:55:54 +0000

A-Course of Mathematics (Paper A & B) This subject is consists of two papers of 100 marks each. One is called “Paper A” and other is called “Paper B”. This page is updated on February 15, 2015. This syllabus is for 1st Annual 2015 and onward organized by University of Sargodha, Sargodha.

Pure Mathematics (Paper A & B)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:55:59 +0000

Pure Mathematics (Paper A & B) This paper consist of two papers of 100 marks each. One paper is called “Paper A” and the other is called “Paper B”. Paper A * NOTE: attempt two questions from each section. SECTION-I (4/12: 17,17,17,17)