This is beta site. https://beta.mathcity.org/ 2026-06-07T10:19:17+00:00 https://beta.mathcity.org/ https://beta.mathcity.org/_media/logo.png text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/notes/method-of-mathematical-physics-m-usman-hamid?rev=1737476041&do=diff 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. text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/notes/mathematical-method-muzammil-tanveer?rev=1737476041&do=diff 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. text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/notes/mathematical-statistics-i-muzammil-tanveer?rev=1737476041&do=diff Mathematical Statistics I by Muzammil Tanveer [Mathematical Statistics I] 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 Mathematical Statistics text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/notes/note-for-numerical-methods-m-usman-hamid?rev=1737476041&do=diff 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)$$\left(\frac{3}{8}\right)$ text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/notes/rings-and-modules-iqra-liaqat?rev=1737476041&do=diff Rings & Modules by Ms. Iqra Liaqat Ring is a mathematical structure with two operations. With one operation it is abelian group and with other operation it is semi-group with distributive law holds with first operation w.r.t the other operation. This concept is of pure in nature in mathematics. These advanced level notes are typically taken as an elective in a mathematics undergraduate degree. text/html 2025-01-21T16:14:02+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/notes/special-functions-muzammil-tanveer?rev=1737476042&do=diff Special Functions by Dr. Muhey-U-Din These notes are provided and composed by Mr. Muzammil Tanveer. We are really very thankful to him for providing these notes and appreciates his effort to publish these notes on MathCity.org. Thease notes are based on the lectures by Dr. Muhey-U-Din. text/html 2025-01-21T16:14:02+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/notes/topology-handwritten-notes?rev=1737476042&do=diff Topology: Handwritten Notes [House of Tau] A topological space is a collection of points with a topology-a structure that describes how close two points are to one another. It is a generalisation of Euclidean spaces that makes it possible to investigate boundaries, continuity, and connectivity. A topology is a group of open sets, or subsets, that adhere to certain principles.$T_0$$T_1$$T_2$$\varepsilon-$ text/html 2025-01-21T16:14:02+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/notes/vector-spaces-review-by-rashad-wattu?rev=1737476042&do=diff 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. text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/notes/advanced-analysis-iqra-liaqat?rev=1737476041&do=diff Advance Analysis by Ms. Iqra Liaqat [Advance Analysis 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 Advance Analysis Sender Ms. Iqra Liaqat Author $\sigma$ text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/notes/analysis?rev=1737476041&do=diff Notes of Analysis advanced-analysis-handwritten-notes Advanced Analysis: Handwritten Notes Advanced-Analysis-iqra-liaqat Advance Analysis by Ms. Iqra Liaqat Complex-Analysis-Dr-Amir-Mahmood Complex Analysis (Easy Notes of Complex Analysis) Complex-Analysis-M-Usman-Hamid Complex Analysis by M Usman Hamid complex-analysis-iqra-liaqat Complex Analysis (Notes) by Ms. Iqra Liaqat Complex-Analysis-Quick-Review Complex Analysis (Quick Review) Akhtar Abbas fundamental-of-complex-… text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/notes/complex-analysis-iqra-liaqat?rev=1737476041&do=diff Complex Analysis (Notes) by Ms. Iqra Liaqat [Notes of Complex Analysis 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 Complex analysis is the study of functions of complex numbers. It is useful in a variety of mathematical fields, such as algebraic geometry, number theory, analytic combinatorics, and applied mathematics, as well as in physics fields like… text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/notes/complex-analysis-quick-review?rev=1737476041&do=diff Complex Analysis (Quick Review) [Complex Analysis: Quick Review] 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. Important definitions and important results are the part of these notes, these might be helpful to prepare interviews or any other written test after graduation like PPSC, FPSC or etc.$z_1, z_2 \in S$$S$$v(x,y)$$u(x,y)$$f(z)=u(x,y)+iv(x,y)$$f$$D$$C$$D$… text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/notes/elementary-linear-algebra-m-usman-hamid?rev=1737476041&do=diff 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… text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/notes/fluid-dynamics-i-m-usman-hamid?rev=1737476041&do=diff Fluid Dynamics I by Muhammad Usman Hamid [Fluid Dynamics I by Muhammad Usman Hamid] These notes are send by Mr. Anwar Khan, PhD. 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 written by Muhammad Usman Hamid. * Name: Fluid Dynamics I text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/notes/fundamental-of-complex-analysis-prof-m-saleem?rev=1737476041&do=diff Fundamental of Complex Analysis (Solutions of Some Exercises) [Fundamental of Complex Analysis, Solutions of Some Exercises] Complex analysis is the study of functions that exist in the complex plane, that is, functions with complex arguments and complex outputs. With roots in the 18th century and the years just before, it is one of the classical branches of mathematics. In the 20th century, significant figures in mathematics who are connected to complex numbers include Euler, Gauss, Riemann, … text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/notes/groups-handwritten-notes?rev=1737476041&do=diff Groups (Handwritten Notes) by Atiq ur Rehman Groups are a basic idea in algebra, introduced in high school. It's a very interesting topic in math. [Cube root of unity group] * Name: Groups (Handwritten notes)- Lecture Notes * Author: Atiq ur Rehman * Pages: 82 pages text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/notes/history-of-mathematics-m-usman-hamid?rev=1737476041&do=diff 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. text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/notes/mathematical-method-usman-hamid?rev=1737476041&do=diff Mathematical Method by Muhammad Usman Hamid [Mathematical Method by Muhammad Usman Hamid] These notes are send by Muhammad Usman Hamid. We acknowledged his efforts to published these notes on MathCity.org. The main objective of this course is to provide the students with a range of mathematical methods that are essential to the solution of advanced problems encountered in the fields of applied physics and engineering. In addition this course is intended to prepare the students with mathematic… text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/notes/measure-theory-by-anwar-khan?rev=1737476041&do=diff Measure Theory Notes by Anwar Khan [Measure Theory Notes by Anwar Khan] Measure theory is a branch of mathematics concerned with the concept of “measure,” which is a method of assigning a numerical value to specific sets. The concepts of length, area, and volume are generalised via measurements to more abstract environments, such as infinite-dimensional spaces and areas that cannot be seen.$X$$\sigma-$$X$$\sigma-$$\sigma-$$\lim\limits_{k\to \infty} \sup A_k$$\lim\limits_{k\to \infty} \inf A_k$… text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/notes/multivariable-calculus-sheikh-muhammad-saleem-shahzad?rev=1737476041&do=diff Multivariable Calculus by Sheikh Muhammad Saleem Shahzad [Multivariable Calculus by Sheikh Muhammad Saleem Shahzad] * Have you ever wondered how we can understand the speed of a moving object at any instant of time? * Did you know that Calculus can help us predict future trends by analyzing patterns in data? text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/notes/partial-differential-equations-m-usman-hamid?rev=1737476041&do=diff Partial Differential Equations 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 text/html 2025-01-21T16:14:02+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/notes/vector_spaces_handwritten_notes?rev=1737476042&do=diff 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. text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/notes/advanced-analysis-handwritten-notes?rev=1737476041&do=diff 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. text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/notes/affine-and-euclidean-geometry-shahzad-idress?rev=1737476041&do=diff 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 $R^n$ text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/notes/algebra?rev=1737476041&do=diff Notes of Algebra All the notes of algebra are given here. [All the notes of algebra] <well> <caption> Algebra II by Syed Sheraz Asghar </caption> A notes of Algebra-II composed by Muzammil Tanveer. We are very thankful to him for sending these notes. </well><well> <caption> Elementary Linear Algebra by Muhammad Usman Hamid </caption> Linear Algebra is the study of vectors and linear transformations. Best notes to prepare the subject written by text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/notes/algebra-ii-by-syed-sheraz-asghar?rev=1737476041&do=diff 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 text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/notes/classical-mechanics-muhammad-usman-hamid?rev=1737476041&do=diff 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. text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/notes/differential-geometry-kaushef_salamat?rev=1737476041&do=diff Differential Geometry (Notes) by Ms. Kaushef Salamat [Differential Geometry by Ms. Kaushef Salamat] Differential Geometry is an important field in the mathematical sciences. Usually, this is a compulsory or core subject for BS mathematics students. These notes are send by Ms. Kaushef Salamat. We are really very thankful to her for providing these notes and appreciates her effort to publish these notes on MathCity.org text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/notes/differential-geometry-m-usman-hamid?rev=1737476041&do=diff 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 text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/notes/functional-analysis-m-usman-hamid-and-zeeshan-ahmad?rev=1737476041&do=diff 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. text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/notes/fuzzy-sets-theory-umar-saeed-bunarai?rev=1737476041&do=diff Fuzzy Sets Theory by Umar Saeed Bunarai [Fuzzy Sets Theory by Umar Saeed Bunarai] In the field of mathematics known as fuzzy set theory, sets having varying degrees of membership are studied. This implies that an element can be a member of a set only partially or not at all. In several disciplines, including logic, control, data analysis, and decision-making, fuzzy set theory is used to model uncertainty, vagueness, and imprecision. text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/notes/general-topolgy-raheel-ahmad?rev=1737476041&do=diff General Topology by Raheel Ahmad A handwritten notes of Topology by Mr. Raheel Ahmad. We are very thankful to him for sending these notes. Name General Topology Author Mr. Raheel Ahmad Pages 87 pages Format Mobile Scanned PDF Size 8.0 MB What is in the notes? text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/notes/groups-theory-m-iftikhar?rev=1737476041&do=diff Group Theory by Mr. Muhammad Iftikhar [Group Theory by Mr. Muhammad Iftikhar] These notes are send by Mr. Muhammad Iftikhar. We are really very thankful to him for providing these notes and appreciates his effort to publish these notes on MathCity.org. Name Lecture Notes on Group Theory Author Mr. Muhammad Iftikhar text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/notes/handwritten-notes-real-analysis-asim-marwat?rev=1737476041&do=diff Handwritten Notes of Real Analysis by Asim Marwat [Handwritten Notes of Real Analysis by Asim Marwat] Real analysis is a branch of mathematics that analyses how real numbers, sequences and series, and real functions behave. It focuses on real numbers and frequently extends the real line by including positive and negative infinity. Real analysis investigates a number of the properties of real-valued sequences and functions, including convergence, limits, continuity, smoothness, differentiabilit… text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/notes/mathematical-statistics-iqra-liaqat?rev=1737476041&do=diff 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 text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/notes/measure-thoery-muhsa?rev=1737476041&do=diff Measure Theory by M Usman Hamid & Saima Akram [Measure Theory by M Usman Hamid & Saima Akram] The study of measures on sets is the focus of the mathematical field known as measure theory. A measure is a function that gives specific subsets of a given set a non-negative real integer, indicating their size inferentially. The concept of measure is a formalisation and generalisation of common concepts like mass and event probability as well as geometrical measurements (length, area, and volume). text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/notes/mechanics-by-sir-nouman-siddique?rev=1737476041&do=diff Mechanics by Sir Nouman Siddique 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: Mechanics * Provider: Mr. Muzammil Tanveer text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/notes/metric-spaces-notes?rev=1737476041&do=diff Metric Spaces (Notes) [Metric Spaces (Notes)] These are updated version of previous notes. Many mistakes and errors have been removed. These notes are collected, composed and corrected by Atiq ur Rehman, PhD. These are actually based on the lectures delivered by Prof. Muhammad Ashfaq (Ex HoD, Department of Mathematics, Government College Sargodha). $(X,d)$$x,y\in X$$$\left| {\,d(x,\,A)\, - \,d(y,\,A)\,} \right|\,\, \le \,\,d(x,\,y).$$$A^c$$A\subset X$$x \in X$$B(x;r)$$A \subset X$$f:(X,d)\to (Y… text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/notes/numerical-analysis-by-m-usman-hamid?rev=1737476041&do=diff Numerical Analysis 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 text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/notes/operation-research-handwritten-notes?rev=1737476041&do=diff 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 … text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/notes/real-analysis-hand-written-kaushef?rev=1737476041&do=diff 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. $\infty$ text/html 2025-01-21T16:14:01+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/notes/real-analysis-notes-by-prof-syed-gul-shah?rev=1737476041&do=diff Real Analysis Notes by Prof Syed Gul Shah [Real Analysis Notes by Prof Syed Gul Shah] Real analysis, a discipline that explores the complexities of mathematical functions, limits, and sequences, can often be a difficult topic for students. Prof. Syed Gul Shah, as a true analyst, not only excelled in the subject but also gained fame for his extraordinary qualities as a human being.$s_n<u_n<t_n$$n\ge n_0$$\{s_n\}$$\{t_n\}$$\{u_n\}$$\{s_n\}$$\exists$$\left| {\,{s_n}}\right|>\frac{1}{2}s$$\{s_n\}$… text/html 2025-01-21T16:14:02+00:00 Anonymous (anonymous@undisclosed.example.com) https://beta.mathcity.org/notes/theory-of-relativity-and-analytic-dynamics?rev=1737476042&do=diff Theory of Relativity & Analytic Dynamics: Handwritten Notes [Theory of Relativity & Analytic Dynamics: Handwritten Notes] Theory of Relativity and Analytic Dynamics is a subject that encompasses two distinct topics: relativity theory and analytic dynamics. Albert Einstein's theory of relativity defines the fundamental principles that control how moving objects behave in relation to one another and to the observer. The motion of objects as a result of forces and torques is the subject of analyt…