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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\}$…

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…

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…

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$

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$…

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. $\infty$

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-$

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$

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…

Quantitative Reasoning-I (QR1: Exploring Quantitative Skills)

anonymous@undisclosed.example.com (Anonymous) — Mon, 15 Dec 2025 16:47:25 +0000

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…