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.

Computing Tools for Mathematics by Asif Arshad

anonymous@undisclosed.example.com (Anonymous) — Sat, 05 Aug 2023 20:30:34 +0000

Computing Tools for Mathematics by Asif Arshad [omputing Tools for Mathematics by Asif Arshad] Computing tools for mathematics are algorithms that use computers to solve mathematical issues. They are employed in a number of scientific, technical, industrial, and technological domains where computer is crucial and central. They may assist in creating precise and effective numerical techniques, for instance, to solve physical or biological models.

Notes of Algebra

anonymous@undisclosed.example.com (Anonymous) — Wed, 26 Jun 2024 18:24:28 +0000

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

Functional Analysis by M Usman Hamid and Zeeshan Ahmad

anonymous@undisclosed.example.com (Anonymous) — Wed, 18 Sep 2024 18:09:17 +0000

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.

Fundamental of Complex Analysis (Solutions of Some Exercises)

anonymous@undisclosed.example.com (Anonymous) — Sat, 15 Apr 2023 18:26:12 +0000

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, …

Handwritten Notes of Real Analysis by Asim Marwat

anonymous@undisclosed.example.com (Anonymous) — Sat, 15 Apr 2023 17:26:13 +0000

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…

Notes for Numerical Methods by M Usman Hamid

anonymous@undisclosed.example.com (Anonymous) — Sat, 05 Aug 2023 17:59:07 +0000

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)$

Fluid Mechanics by Ali Raza

anonymous@undisclosed.example.com (Anonymous) — Sat, 27 Jul 2024 16:23:08 +0000

Fluid Mechanics by Ali Raza [Fluid Mechanics by Ali Raza] Fluid mechanics is the branch of physics that studies how fluids (liquids, gases, and plasmas) behave and interact with forces and energy. Fluid mechanics has many applications in engineering, geophysics, biology, and other fields.

Functional Analysis by Prof Mumtaz Ahmad

anonymous@undisclosed.example.com (Anonymous) — Wed, 18 Sep 2024 18:11:56 +0000

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$

Mathematical Statistics II by Sir Haidar Ali

anonymous@undisclosed.example.com (Anonymous) — Thu, 20 Apr 2023 12:16:43 +0000

Mathematical Statistics II by Sir Haidar Ali [Mathematical Statistics II] A subfield of mathematics called mathematical statistics is concerned with using mathematical techniques to solve statistical problems. It involves using mathematical analysis and probability theory to the study of statistical issues like estimate, hypothesis testing, and confidence intervals. Financial, engineering, and scientific fields all benefit from the use of mathematical statistics, which is a significant area of…

Measure Theory Notes by Anwar Khan

anonymous@undisclosed.example.com (Anonymous) — Mon, 01 May 2023 13:54:40 +0000

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$…

Mechanics I (Statics) by Dr Babar Ahmad

anonymous@undisclosed.example.com (Anonymous) — Mon, 24 Jul 2023 12:49:29 +0000

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.

Number Theory: Handwritten Notes

anonymous@undisclosed.example.com (Anonymous) — Tue, 08 Aug 2023 11:20:45 +0000

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

Number Theory Notes by Anwar Khan

anonymous@undisclosed.example.com (Anonymous) — Sat, 05 Aug 2023 18:47:01 +0000

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…

Number Theory by Dr Muhammad Umer Shuaib

anonymous@undisclosed.example.com (Anonymous) — Sat, 05 Aug 2023 18:11:04 +0000

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.$\phi$

Numerical Analysis by M Usman Hamid

anonymous@undisclosed.example.com (Anonymous) — Sat, 05 Aug 2023 17:01:51 +0000

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

Rings & Modules by Ms. Iqra Liaqat

anonymous@undisclosed.example.com (Anonymous) — Sat, 01 Apr 2023 14:30:33 +0000

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.

Theory of Optimization by Ma'am Iqra Razzaq

anonymous@undisclosed.example.com (Anonymous) — Sun, 23 Jul 2023 16:28:59 +0000

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.

Advanced Analysis: Handwritten Notes

anonymous@undisclosed.example.com (Anonymous) — Fri, 14 Apr 2023 17:55:33 +0000

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.

Algebraic Number Theory Notes by Anwar Khan

anonymous@undisclosed.example.com (Anonymous) — Sat, 05 Aug 2023 19:06:20 +0000

Algebraic Number Theory Notes by Anwar Khan [Algebraic Number Theory Notes by Anwar Khan] Algebraic number theory is a subfield of number theory that studies integers, rational numbers, and their generalisations using abstract algebra techniques. It covers Galois theory, ideals and units in rings of integers, unique factorization, and algebraic number fields and related rings of integers. It is a complex and in-depth subject with numerous linkages to other branches of mathematics.$\mathbb{R}$

Complex Analysis (Easy Notes of Complex Analysis)

anonymous@undisclosed.example.com (Anonymous) — Sun, 06 Aug 2023 11:17:51 +0000

Complex Analysis (Easy Notes of Complex Analysis) [Complex Analysis (Easy Notes of Complex Analysis) ] The study of complex numbers, together with their manipulation, derivatives, and other characteristics, is known as complex integration. Contour integration is a technique for analysing specific integrals along pathways in the complex plane in the field of complex analysis mathematics. The complex analytic technique known as the calculus of residues and contour integration are closely linked.

Complex Analysis (Notes) by Ms. Iqra Liaqat

anonymous@undisclosed.example.com (Anonymous) — Sun, 06 Aug 2023 09:33:02 +0000

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…

Complex Analysis by M Usman Hamid

anonymous@undisclosed.example.com (Anonymous) — Sat, 08 Feb 2025 08:11:42 +0000

Complex Analysis by M Usman Hamid [Complex Analysis by M Usman Hamid] We are really very thankful to Muhammad Usman Hamid for providing these notes and appreciates his effort to publish these notes on MathCity.org It covers the one part of the syllabus of Complex Analysis paper of MSc Mathematics. See the contents of the notes given below to see the topics covered by these notes.$$ x^2+4=0, x^2+x+1=0 \text{ and } x^2-2x+3=0 $$$i=\sqrt{-1}$$i^2=-1$

Differential Geometry: Handwritten Notes

anonymous@undisclosed.example.com (Anonymous) — Sat, 23 Aug 2025 11:27:57 +0000

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 …

Differential Geometry (Notes) by Ms. Kaushef Salamat

anonymous@undisclosed.example.com (Anonymous) — Sat, 23 Aug 2025 11:29:10 +0000

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

Differential Geometry by M Usman Hamid

anonymous@undisclosed.example.com (Anonymous) — Sat, 23 Aug 2025 11:29:44 +0000

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

Differential Geometry by Syed Hassan Waqas

anonymous@undisclosed.example.com (Anonymous) — Sat, 23 Aug 2025 11:28:41 +0000

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.…

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…

Functional Analysis by Mr. Tahir Hussain Jaffery

anonymous@undisclosed.example.com (Anonymous) — Wed, 18 Sep 2024 18:13:33 +0000

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$

Fuzzy Sets Theory by Umar Saeed Bunarai

anonymous@undisclosed.example.com (Anonymous) — Tue, 08 Aug 2023 11:56:34 +0000

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.

Mathematical Method by Sir Muhammad Awais Aun

anonymous@undisclosed.example.com (Anonymous) — Mon, 17 Apr 2023 09:02:35 +0000

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.

Measure Theory Handwritten Notes by Asim Marwat

anonymous@undisclosed.example.com (Anonymous) — Fri, 10 Feb 2023 17:43:56 +0000

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$

Measure Theory by M Usman Hamid & Saima Akram

anonymous@undisclosed.example.com (Anonymous) — Wed, 26 Jun 2024 17:55:59 +0000

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).

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.

Method of Mathematical Physics by Mr. Muhammad Usman Hamid

anonymous@undisclosed.example.com (Anonymous) — Thu, 20 Apr 2023 11:54:01 +0000

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.

Metric Spaces (Notes)

anonymous@undisclosed.example.com (Anonymous) — Fri, 18 Aug 2023 18:05:58 +0000

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…

Multivariable Calculus by M Usman Hamid and M Zeeshan Ahmad

anonymous@undisclosed.example.com (Anonymous) — Sun, 15 Jun 2025 16:25:59 +0000

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…

Multivariable Calculus by Sheikh Muhammad Saleem Shahzad

anonymous@undisclosed.example.com (Anonymous) — Sun, 17 Dec 2023 17:13:50 +0000

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?

Real Analysis Handwritten Notes by Kaushef Salamat

anonymous@undisclosed.example.com (Anonymous) — Fri, 20 Jan 2023 17:26:27 +0000

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. $\infty$

Real Analysis Notes by Prof Syed Gul Shah

anonymous@undisclosed.example.com (Anonymous) — Mon, 17 Apr 2023 04:04:23 +0000

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\frac{1}{2}s$$\{s_n\}$…

Ring (Notes) by Prof. M. Dabeer Mughal

anonymous@undisclosed.example.com (Anonymous) — Sat, 01 Apr 2023 06:56:21 +0000

Ring (Notes) by Prof. M. Dabeer Mughal [Ring (Notes) by Prof. M. Dabeer Mughal] A handwritten notes on Ring (Algebra) by Prof. M. Dabeer Mughal (Federal Directorate of Education, Islamabad, Pakistan). It is best to prepare a “Rings and Vector Spaces” section of your algebra paper or Algebra II for BS or MS Mathematics.$\phi$

Topology and Functional Analysis Solved Paper by Noman Khalid

anonymous@undisclosed.example.com (Anonymous) — Sun, 11 Feb 2024 12:38:09 +0000

Topology and Functional Analysis Solved Paper by Noman Khalid These solved papers are written and provided by Mr. noman-khalid. We are very thankful to him for providing these notes to publish on MathCity.org. Topology and Functional Analysis is considered as one the tough subject in BS/MSc Mathematics in different universities. Here solved paper for the said subject is given for the University of the Punjab (PU), Lahore.

Topology: Handwritten Notes

anonymous@undisclosed.example.com (Anonymous) — Sat, 01 Mar 2025 09:43:45 +0000

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-$

Vector Spaces (Handwritten notes)

anonymous@undisclosed.example.com (Anonymous) — Sat, 01 Apr 2023 15:18:56 +0000

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.