Merging man & maths https://www.mathcity.org/ Thu, 04 Jun 2026 02:43:51 +0000 FeedCreator 1.8 https://www.mathcity.org/_media/logo.svg https://www.mathcity.org/ https://www.mathcity.org/notes/elementary-linear-algebra-m-usman-hamid 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… anonymous@undisclosed.example.com (Anonymous) Sun, 10 Dec 2023 14:05:12 +0000 https://www.mathcity.org/notes/functional-analysis-by-tahir-hussain-jaffery Functional Analysis by Mr. Tahir Hussain Jaffery [Functional Analysis by Prof Mumtaz Ahmad] Functional analysis is a branch of mathematics concerned with vector space theory and linear algebra. It requires looking into the relationships between various roles, objects, incidents, actions, and results. The term $M$$M+N$ anonymous@undisclosed.example.com (Anonymous) Wed, 18 Sep 2024 18:13:33 +0000 https://www.mathcity.org/notes/linear-algebra-important-definitions-and-results Linear Algebra: Important Definitions and Results [Linear Algebra: Important Definitions and Results] These notes are made and shared by Mr. Akhtar Abbas. We are really very thankful to him for providing these notes and appreciates his efforts to publish these notes on MathCity.org. These notes contains important definitions with examples and related theorem, which might be helpful to prepare interviews or any other written test after graduation like PPSC, FPSC or etc.$V$$n$$n$$V$$W$$V$$A$$A$$A… anonymous@undisclosed.example.com (Anonymous) Wed, 10 Aug 2022 16:49:49 +0000 https://www.mathcity.org/notes/qr2-tools-for-quantitative-reasoning-m-usman-hamid Quantitative Reasoning II (QR2: Tools for Reasoning Skills) [Quantitative Reasoning II (Tools for Reasoning Skills)] This handout provides a comprehensive exploration of fundamental mathematical and logical concepts, making it an essential read for students and professionals alike. It begins with an introduction to enumeration and its practical applications, followed by an in-depth discussion on quantitative reasoning, number systems, and arithmetic operations. The book highlights the contribut… anonymous@undisclosed.example.com (Anonymous) Fri, 01 Aug 2025 18:31:56 +0000 https://www.mathcity.org/notes/topology-handwritten-notes Topology: Handwritten Notes [House of Tau] A topological space is a collection of points with a topology-a structure that describes how close two points are to one another. It is a generalisation of Euclidean spaces that makes it possible to investigate boundaries, continuity, and connectivity. A topology is a group of open sets, or subsets, that adhere to certain principles.$T_0$$T_1$$T_2$$\varepsilon-$ anonymous@undisclosed.example.com (Anonymous) Sat, 01 Mar 2025 09:43:45 +0000 https://www.mathcity.org/notes/algebra-ii-by-syed-sheraz-asghar Algebra II by Syed Sheraz Asghar [Algebra II by Syed Sheraz Asghar] These notes are provided and composed by Mr. Muzammil Tanveer. We are really very thankful to him for providing these notes and appreciates his effort to publish these notes on MathCity.org * Name: Algebra II * Provider: Mr. Muzammil Tanveer anonymous@undisclosed.example.com (Anonymous) Sun, 10 Dec 2023 14:02:42 +0000 https://www.mathcity.org/notes/operation-research-haidar-ali Operation Research by Sir Haidar Ali [Notes of Operation Research by Sir Haidar Ali] These notes are provided and composed by Mr. Muzammil Tanveer. We are really very thankful to him for providing these notes and appreciates his effort to publish these notes on MathCity.org. These are based on lectures delivered by Sir Haidar Ali at GC University Faisalabad. anonymous@undisclosed.example.com (Anonymous) Fri, 21 Mar 2025 17:42:28 +0000 https://www.mathcity.org/notes/classical-mechanics-muhammad-usman-hamid Classical Mechanics by Muhammad Usman Hamid [Classical Mechanics by Muhammad Usman Hamid] Objectives of the course: To provide solid understanding of classical mechanics and enable the students to use this understanding while studying courses on quantum mechanics, statistical mechanics, electromagnetism, fluid dynamics, space-flight dynamics, astrodynamics and continuum mechanics. anonymous@undisclosed.example.com (Anonymous) Mon, 29 Jul 2024 18:38:28 +0000 https://www.mathcity.org/notes/functional-analysis-m-usman-hamid-and-zeeshan-ahmad Functional Analysis by M Usman Hamid and Zeeshan Ahmad [Functional Analysis by M Usman Hamid and Zeeshan Ahmad] These notes are send by Muhammad Usman Hamid and written by Muhammad Usman Hamid and Zeeshan Ahmad. We are really very thankful to him for providing these notes and appreciate his effort to publish these notes on MathCity.org. Usman is dedicated and committed mathematician, who is working very hard for better understanding of mathematics to it readers. anonymous@undisclosed.example.com (Anonymous) Wed, 18 Sep 2024 18:09:17 +0000 https://www.mathcity.org/notes/algebra Notes of Algebra All the notes of algebra are given here. [All the notes of algebra] Algebra II by Syed Sheraz Asghar A notes of Algebra-II composed by Muzammil Tanveer. We are very thankful to him for sending these notes. Elementary Linear Algebra by Muhammad Usman Hamid Linear Algebra is the study of vectors and linear transformations. Best notes to prepare the subject written by anonymous@undisclosed.example.com (Anonymous) Wed, 26 Jun 2024 18:24:28 +0000 https://www.mathcity.org/notes/method-of-mathematical-physics-m-usman-hamid Method of Mathematical Physics by Mr. Muhammad Usman Hamid [Method of Mathematical Physics by Mr. Muhammad Usman Hamid] Method of Mathematical Physics is an area of mathematics concerned with the application of mathematical methods to physics problems. Mathematical techniques for statistical mechanics, quantum mechanics, and classical mechanics are all included in this large field. anonymous@undisclosed.example.com (Anonymous) Thu, 20 Apr 2023 11:54:01 +0000 https://www.mathcity.org/notes/vector_spaces_handwritten_notes Vector Spaces (Handwritten notes) [Vector Spaces (Handwritten notes) by Atiq ur Rehman] Vector space is a fundamental subject in mathematics. At the undergraduate and upper secondary levels, the concept of vector space is regarded as basic and fundamental. These are lecture notes of Prof. Dr. Muhammad Khalid of University of Sargodha, Sargodha written by Atiq ur Rehman. anonymous@undisclosed.example.com (Anonymous) Sat, 01 Apr 2023 15:18:56 +0000 https://www.mathcity.org/notes/vector-and-tensor-analysis-by-dr-nawazish Vector & Tensor Analysis by Dr Nawazish Ali (Solutions) [Vector & Tensor Analysis by Dr Nawazish Ali (Solutions)] We are very thankful to Prof. Fazal Abbas Sajid for sharing these solutions. Vector & Tensor Analysis for Scientists and Engineers, by Prof. Dr. Nawazish Ali Shah is a famous book taught in different universities of the Pakistan. On this page, we have added the solutions of the exercises of the book. Solutions of Chapter 5 is written by anonymous@undisclosed.example.com (Anonymous) Sun, 06 Aug 2023 18:20:39 +0000 https://www.mathcity.org/notes/vector-and-tensor-analysis-by-prof-fazal-abbas Vector & Tensor Analysis by Prof Fazal Abbas [Vector & Tensor Analysis by Prof Fazal Abbas] Solution of Chapter 6: Curvilinear Coordinates of the book Vector & Tensor Analysis by Prof. Dr. Nawazish Ali Shah written by Prof. Fazal Abbas Sajid. Here solutions of chapter 6 are provided by the author of the book, for the solutions of all the chapters of the book, please buy the solution manual from the market. anonymous@undisclosed.example.com (Anonymous) Wed, 24 Aug 2022 07:12:53 +0000 https://www.mathcity.org/notes/vector-spaces-review-by-rashad-wattu Vector Space (Review) by Rashad Wattu Mathematical vector space is a crucial and fundamental idea. It depends on the concept of field. These notes were primarily written to help maths students understand vector space, which is a concept that they all need to be familiar with. anonymous@undisclosed.example.com (Anonymous) Sat, 01 Apr 2023 14:51:01 +0000 https://www.mathcity.org/notes/functional-analysis-by-prof-mumtaz-ahmad Functional Analysis by Prof Mumtaz Ahmad [Functional Analysis by Prof Mumtaz Ahmad] Functional analysis is a subfield of mathematics that deals with vector space theory and linear algebra. It entails researching the connections between roles, things, incidents, actions, and outcomes. The word $l^\infty$$l^\infty$ anonymous@undisclosed.example.com (Anonymous) Wed, 18 Sep 2024 18:11:56 +0000 https://www.mathcity.org/notes/note-for-numerical-methods-m-usman-hamid Notes for Numerical Methods by M Usman Hamid [Notes for Numerical Methods by M Usman Hamid] These notes are initially provided by Mr. Anwar Khan. Later the updated version is send by Muhammad Tahir. We are really very thankful to Mr. Anwar Khan and Muhammad Tahir for providing these notes and appreciates their effort to publish these notes on MathCity.org$\left(\frac{1}{3}\right)$$\left(\frac{3}{8}\right)$ anonymous@undisclosed.example.com (Anonymous) Sat, 05 Aug 2023 17:59:07 +0000 https://www.mathcity.org/notes/partial-differential-equations-m-usman-hamid Partial Differential Equations (PDE) by M Usman Hamid The course provides a foundation to solve PDE’s with special emphasis on wave, heat and Laplace equations, formulation and some theory of these equations are also intended. We are really very thankful to Prof. Muhammad Usman Hamid for providing these notes and appreciates his effort to publish these notes on MathCity.org anonymous@undisclosed.example.com (Anonymous) Sun, 09 Mar 2025 09:27:42 +0000 https://www.mathcity.org/notes/affine-and-euclidean-geometry-shahzad-idress Affine and Euclidean Geometry by Shahzad Idress [Affine and Euclidean Geometry by Shahzad Idress] These notes are sent by shahzad-idress. We acknowledged his efforts to published these notes on MathCity.org. These are short notes containing topics related to Affine and Euclidean Geometry. The main sections includes $R^n$ anonymous@undisclosed.example.com (Anonymous) Mon, 24 Jul 2023 10:30:52 +0000 https://www.mathcity.org/notes/differential_geometry_notes Differential Geometry: Handwritten Notes [Differential Geometry: Handwritten Notes] Differential geometry is a discipline of mathematics that investigates the geometry of smooth objects and spaces, sometimes known as smooth manifolds. It investigates the geometric properties of curves and surfaces using the methods of differential and integral calculus, linear algebra, and multilinear algebra. Mathematical analysis and differential geometry are related concepts. These are the lecture notes of … anonymous@undisclosed.example.com (Anonymous) Sat, 23 Aug 2025 11:27:57 +0000 https://www.mathcity.org/notes/differential-geometry-syed-hassan-waqas Differential Geometry by Syed Hassan Waqas [Differential Geometry by Syed Hassan Waqas] In the field of mathematics known as differential geometry, smooth manifolds—also known as smooth shapes and spaces—and their geometry are studied. Investigating the geometric characteristics of curves and surfaces involves the use of the tools of differential and integral calculus, linear algebra, and multilinear algebra. Differential calculus and mathematical analysis are related to differential geometry.… anonymous@undisclosed.example.com (Anonymous) Sat, 23 Aug 2025 11:28:41 +0000 https://www.mathcity.org/notes/mathematical-method-muzammil-tanveer Mathematical Method by Sir Muhammad Awais Aun [Mathematical Method by Muzammil Tanveer] Mathematical methods are the approaches employed by mathematicians to address issues in mathematics and science. Algebra, functions, relations and associated graphs, calculus, and statistics are examples of mathematical techniques. Through their usage in resolving practical issues, they are applied to modelling. anonymous@undisclosed.example.com (Anonymous) Mon, 17 Apr 2023 09:02:35 +0000 https://www.mathcity.org/notes/mechanics-i-statics-dr-babar-ahmad Mechanics I (Statics) by Dr Babar Ahmad [Mechanics I (Statics) 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. anonymous@undisclosed.example.com (Anonymous) Mon, 24 Jul 2023 12:49:29 +0000 https://www.mathcity.org/notes/multivariable-calculus-m-usman-hamid-and-m-zeeshan-ahmad Multivariable Calculus by M Usman Hamid and M Zeeshan Ahmad [Multivariable Calculus by M Usman Hamid and M Zeeshan Ahmad] Multivariable calculus is a fundamental subject that extends the concepts of single-variable calculus to higher-dimensional spaces. It provides a powerful framework for analyzing and modeling complex phenomena in fields such as physics, engineering, economics, and computer science. This textbook is designed to provide a comprehensive introduction to multivariable calculus, c… anonymous@undisclosed.example.com (Anonymous) Sun, 15 Jun 2025 16:25:59 +0000 https://www.mathcity.org/notes/number-theory-umer-shuaib Number Theory by Dr Muhammad Umer Shuaib [Number Theory Notes] A subfield of mathematics called number theory studies the characteristics of positive integers. Higher arithmetic is another name for it. The study of the relationships between various types of numbers, including prime numbers, rational numbers, and algebraic integers, is done using number theory, one of the oldest fields of mathematics.$\phi$ anonymous@undisclosed.example.com (Anonymous) Sat, 05 Aug 2023 18:11:04 +0000 https://www.mathcity.org/notes/numerical-analysis-ii Numerical Analysis II [Numerical Analysis by Muzammil Tanveer] These notes are provided and composed by Mr. Muzammil Tanveer. We are really very thankful to him for providing these notes and appreciates his effort to publish these notes on MathCity.org. Name Numerical Analysis II Compiled by Muzammil Tanveer anonymous@undisclosed.example.com (Anonymous) Sat, 05 Aug 2023 17:56:32 +0000 https://www.mathcity.org/notes/operation-research-handwritten-notes Operation Research: Handwritten Notes [Operation Research: Handwritten Notes] Operation research (OR) is a scientific field that enhances organisational decision-making and problem-solving via the application of mathematical and analytical techniques. The management and administration of many processes, including military, governmental, economic, and industrial ones, include the use of scientific principles. OR is carried out by a group of professionals from various linked fields, depending on … anonymous@undisclosed.example.com (Anonymous) Sat, 05 Aug 2023 16:53:29 +0000 https://www.mathcity.org/notes/ordinary-differential-equations-hamad-safi Ordinary Differential Equations (ODE) by Hammad Safi [Ordinary Differential Equations by Hammad Safi] An equation containing the derivatives of one or more dependent variables with respect to one or more independent variables is said to be a differential equation or a differential equation is an equation which contains one or more terms and derivatives of one or more dependent variables with respect to other variables (independent variables) or an equation that contains derivatives of dependent… anonymous@undisclosed.example.com (Anonymous) Sun, 09 Mar 2025 09:26:46 +0000 https://www.mathcity.org/notes/theory-of-optimization-muzammil-tanveer Theory of Optimization by Ma'am Iqra Razzaq [Special Theory of Optimization by Ma'am Iqra Razzaq] These notes are provided and composed by Mr. Muzammil Tanveer. We are really very thankful to him for providing these notes and appreciates his effort to publish these notes on MathCity.org. These notes are based on the lectures by Ma'am Iqra Razzaq. anonymous@undisclosed.example.com (Anonymous) Sun, 23 Jul 2023 16:28:59 +0000 https://www.mathcity.org/notes/advanced-analysis-handwritten-notes Advanced Analysis: Handwritten Notes [Advanced Analysis: Handwritten Notes] These notes are provided by Mr. Anwar Khan. We are really very thankful to Mr. Anwar Khan for providing these notes and appreciates his effort to publish these notes on MathCity.org It covers the complete syllabus of Advanced Analysis paper of MSc Mathematics. See the contents of the notes given below to see the topics covered by these notes. anonymous@undisclosed.example.com (Anonymous) Fri, 14 Apr 2023 17:55:33 +0000 https://www.mathcity.org/notes/differential-geometry-m-usman-hamid Differential Geometry by M Usman Hamid [Differential Geometry by M Usman Hamid] These notes are initially provided by Mr. Anwar Khan. Later send by many persons. We are really very thankful to all for providing these notes and appreciates their effort to publish these notes on MathCity.org anonymous@undisclosed.example.com (Anonymous) Sat, 23 Aug 2025 11:29:44 +0000 https://www.mathcity.org/notes/fluid-dynamics-i-m-usman-hamid 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. anonymous@undisclosed.example.com (Anonymous) Sun, 03 May 2026 08:26:32 +0000 https://www.mathcity.org/notes/mathematical-statistics-iqra-liaqat Mathematical Statistics by Ms. Iqra Liaqat [Mathematical Statistics by Ms. Iqra Liaqat] These notes are send by Ms. Iqra Liaqat. We are really very thankful to her for providing these notes and appreciates her effort to publish these notes on MathCity.org Name Mathematical Statistics Provided by anonymous@undisclosed.example.com (Anonymous) Thu, 20 Apr 2023 12:30:11 +0000 https://www.mathcity.org/notes/measure-theory-notes-asim-marwat Measure Theory Handwritten Notes by Asim Marwat [Measure Theory Notes by Asim Marwat] These notes are made and shared by Mr. Asim Marwat. He has our sincere gratitude for supplying these notes, and we value his effort in having them published on MathCity.org. Measure Theory is an important subject in BS Mathematics. These notes contain topic from base level, like equivalence set, to advance level, like convergent in measure.$L_p$$L_p$$L^\infty$$L_p$ anonymous@undisclosed.example.com (Anonymous) Fri, 10 Feb 2023 17:43:56 +0000 https://www.mathcity.org/notes/mechanics-ii-analytic-dynamics-i-dr-babar-ahmad Mechanics II (Analytic Dynamics I) by Dr Babar Ahmad [Mechanics II (Analytic Dynamics I) by Dr Babar Ahmad] We are very thankful to Dr Babar Ahmad for sharing his book on MathCity.org. This book is very helpful for undergraduate students of Science and Engineering Programs. This book is shared by the permission of the author and he keeps the copyright of the book. anonymous@undisclosed.example.com (Anonymous) Sat, 24 May 2025 18:13:54 +0000 https://www.mathcity.org/notes/mechanics-iii-analytic-dynamics-ii-dr-babar-ahmad Mechanics III (Analytic Dynamics II) by Dr Babar Ahmad [Mechanics III (Analytic Dynamics II) by Dr Babar Ahmad] We are very thankful to Dr Babar Ahmad for sharing his book on MathCity.org. This book is very helpful for undergraduate students of Science and Engineering Programs. This book is shared by the permission of the author and he keeps the copyright of the book. anonymous@undisclosed.example.com (Anonymous) Sat, 10 May 2025 17:33:01 +0000 https://www.mathcity.org/notes/multiple-choice-questions-bsc-bs-ppsc-akhtar-abbas Multiple Choice Questions (BSc/BS/PPSC) by Akhtar Abbas [Multiple Choice Questions (BSc/BS/PPSC)] These notes are made and shared by Mr. Akhtar Abbas. We are really very thankful to him for providing these notes and appreciates his efforts to publish these notes on MathCity.org. Multiple Choice Questions (MCQs) are given in these notes, which might be helpful in BSc, BS or Punjab Public Service Commission (PPSC) exams.$a$$b$$n$$na > b$$(p − 1)! \equiv −1(mod p)$$p$$p$$p$ anonymous@undisclosed.example.com (Anonymous) Sun, 24 May 2026 17:45:10 +0000 https://www.mathcity.org/notes/number-theory-handwritten-notes Number Theory: Handwritten Notes [Number Theory: Handwritten Notes] The study of the characteristics of the positive integers (1, 2, 3,...) is called number theory. It is significant because it has numerous uses in coding theory, combinatorics, cryptography, and other branches of mathematics and computer science. Some mathematicians also refer to number theory as the anonymous@undisclosed.example.com (Anonymous) Tue, 08 Aug 2023 11:20:45 +0000 https://www.mathcity.org/notes/number-theory-notes-anwar-khan Number Theory Notes by Anwar Khan [Number Theory Notes by Anwar Khan] Mathematicians who specialize in number theory examine the characteristics and connections between integers. “Higher arithmetic” and “the queen of mathematics” are some names for it. Because it examines the characteristics and connections between integers and arithmetic functions, number theory is interesting. It has numerous uses in coding theory, combinatorics, cryptography, and other branches of mathematics. Like the ones… anonymous@undisclosed.example.com (Anonymous) Sat, 05 Aug 2023 18:47:01 +0000 https://www.mathcity.org/notes/partial-differential-equations-muzammil-tanveer Partial Differential Equations (PDE) by Muzammil Tanveer [Partial Differential Equations] These notes are provided and composed by Mr. Muzammil Tanveer. We are really very thankful to him for providing these notes and appreciates his effort to publish these notes on MathCity.org Name: Partial Differential Equations or PDEs anonymous@undisclosed.example.com (Anonymous) Sun, 09 Mar 2025 09:29:35 +0000 https://www.mathcity.org/notes/qr1-exploring-quantitative-skills-m-usman-hamid Quantitative Reasoning-I (QR1: Exploring Quantitative Skills) [Quantitative Reasoning-I (Exploring Quantitative Skills) by M Usman Hamid] This handout offers a comprehensive introduction to numeracy and quantitative reasoning, laying a solid foundation for analytical thinking. It explores fundamental concepts, from basic arithmetic and unit analysis to more advanced topics like probability and statistics. A unique highlight is its exploration of the contributions of mathematicians and statis… anonymous@undisclosed.example.com (Anonymous) Mon, 15 Dec 2025 16:47:25 +0000 https://www.mathcity.org/notes/real-analysis-hand-written-kaushef Real Analysis Handwritten Notes by Kaushef Salamat [Real Analysis Handwritten Notes by Kaushef Salamat] We are very thankful to Ms. Kaushef Salamat for providing these notes. Real Analysis is a core subject in BS or MSc Mathematics. Without a fundamental grasp of Real Analysis, one cannot claim to be a mathematician. These notes are very comprehensive containing almost all the notions of Real Analysis. For providing these notes, Ms. $\infty$ anonymous@undisclosed.example.com (Anonymous) Fri, 20 Jan 2023 17:26:27 +0000 https://www.mathcity.org/notes/rings-and-modules-iqra-liaqat Rings & Modules by Ms. Iqra Liaqat Ring is a mathematical structure with two operations. With one operation it is abelian group and with other operation it is semi-group with distributive law holds with first operation w.r.t the other operation. This concept is of pure in nature in mathematics. These advanced level notes are typically taken as an elective in a mathematics undergraduate degree. anonymous@undisclosed.example.com (Anonymous) Sat, 01 Apr 2023 14:30:33 +0000