MathCity.org

Quotes for the March

anonymous@undisclosed.example.com (Anonymous) — Fri, 28 Apr 2023 18:08:23 +0000

Quotes for the March “نئی ریاضی” کی اہمیت بنیادی طور پر اس حقیقت میں پنہاں ہے کہ اس نے ہمیں ڈسک اور دائرے کے درمیان فرق سکھایا ہے۔ [اسحاق ٹودھنٹر (1820-1884)]

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۔۔۔

Quotes for the April

anonymous@undisclosed.example.com (Anonymous) — Fri, 28 Apr 2023 18:32:46 +0000

Quotes for the April کاسمولوجسٹ اکثر غلط ہوتے ہیں، لیکن کبھی شک میں نہیں۔۔۔ لیو لینڈاؤ (1908-1968) Cosmologists are often wrong, but never in doubt. --- Lev Landau (1908-1968) (Courtesy: MacTutor)

Quotes for the February

anonymous@undisclosed.example.com (Anonymous) — Wed, 22 Feb 2023 16:02:58 +0000

Quotes for the February An expert is someone who knows some of the worst mistakes that can be made in his subject, and how to avoid them [Werner Heisenberg (1901-1976)] ایک ماہر وہ ہوتا ہے جو اپنے مضمون میں ہونے والی کچھ بدترین غلطیوں اور ان سے بچنے کا طریقہ جانتا ہو [ورنر ہیزنبرگ (1901-1976)]

Chapter 06: Plane Curves I

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:45:31 +0000

Chapter 06: Plane Curves I Notes of the book Calculus with Analytic Geometry written by Dr. S. M. Yusuf and Prof. Muhammad Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. [Conic section] Contents and summary * Conic sections * The parabola * The ellipse

About Us

anonymous@undisclosed.example.com (Anonymous) — Thu, 03 Apr 2025 19:07:53 +0000

About Us The only purpose of this website is to help students to learn mathematics. This site contains material for the students of F.Sc., B.Sc., M.Sc., M.Phil. and Ph.D, in the subject of mathematics. The website division has been made according to the different classes for simple navigation. For example, student or teacher searching for notes of F.Sc may see

Dr. Junaid Alam Khan

anonymous@undisclosed.example.com (Anonymous) — Thu, 23 Feb 2023 17:55:59 +0000

Dr. Junaid Alam Khan This is a personal web page of Dr. Junaid Alam Khan Associate Professor Institute of Business Administration, Karachi - PAKISTAN. IBA Profile: ResearchGate Profile: Facebook: [Dr Junaid Alam Khan] Procedure to Compute Sasbi-Standard Bases

Participate

anonymous@undisclosed.example.com (Anonymous) — Sun, 31 May 2026 09:56:03 +0000

Participate If you have written notes, then why not share on MathCity.org with others. This is your help to mathematics students and teachers (یہ صدقہ جاریہ ہے). For further details, please contact webmaster for more information. * The material given on MathCity.org is free and publish to help the students to learn Mathematics. It will take a lot of time to manage this website and prepare new material to publish on this website.

Dr. Muhammad Ahsan Binyamin

anonymous@undisclosed.example.com (Anonymous) — Sun, 19 Feb 2023 08:05:44 +0000

Dr. Muhammad Ahsan Binyamin This is a personal web page of Dr. Muhammad Ahsan Binyamin Associate Professor Government College University Faisalabad, Faisalabad - PAKISTAN. Google Scholar: ResearchGate Profile: Compute Codimension and Milnor number

Fundamental of Complex Analysis: Viewer

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 17:00:41 +0000

Fundamental of Complex Analysis: Viewer Solutions of some exercises from Fundamental of Complex Analysis written by Dr. M. Iqbal and published by Ilmi Kitab Khana, Lahore- PAKISTAN. These are handwritten notes by Prof.(Rtd) Muhammad Saleem. You can also download PDF of solutions from this page.

Tests by Mobeen Munir

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:41:13 +0000

Tests by Mobeen Munir Calculus Chapter 01 ARW Chapter 1,2 & 5 (Important Questions) NEW Download PDF (6KB) ARW Chapter 01, Test 01 Download PDF (51KB) Method Chapter 01 ARW Chapter 01, Test 03 Download PDF (52KB) Chapter 03 ARW Chapter 03, Test 01 Download PDF (67KB) Calculus & Methods (Mixed)

Chapter 04: Techniques of Integration

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:45:30 +0000

Chapter 04: Techniques of Integration These notes are written by Prof. Muhammad Farooq. We are very thankful to him for providing these notes. * Anti-derivative * Table of integrals * Integration by substitution * Integration by parts * Column (or tabular) integration

Chapter 04: Viewer

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:52:02 +0000

Chapter 04: Viewer These notes are written by Prof. Muhammad Farooq. We are very thankful to him for providing these notes. List of all exercises of chapter 04 * Solution of Exercise 4.1 * Solution of Exercise 4.2 * Solution of Exercise 4.3 * Solution of Exercise 4.4 * Solution of Exercise 4.5 * Solution of Exercise 4.6

Privacy & Cookies Policy

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:39:41 +0000

Privacy & Cookies Policy The privacy of our visitors to mathcity.org is important to us. At mathcity.org, we recognize that privacy of your personal information is important. Here is information on what types of personal information we receive and collect when you use and visit mathcity.org, and how we safeguard your information. We never sell your personal information to third parties.

FSc Part 1 Model Papers

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:42:38 +0000

FSc Part 1 Model Papers Federal Board of Intermediate & Secondary Education, Islamabad ARW Model Paper 2008 View Online Download PDF (69KB) ARW Official Model Paper (with solution) View Online Download PDF (154KB) ARW Model Paper 1 (Old) View Online Download PDF (103KB) ARW Model Paper 2 (Old) View Online Download PDF (96KB)

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.

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$

Vector Analysis by Hameed Ullah: Notes

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:41:13 +0000

Vector Analysis by Hameed Ullah: Notes [right triangle in semi circle] Note of vector analysis by Hammed Ullah. These notes are send by Umer Asghar, we are very thankful to him for providing these notes. These notes are for helpful for undergraduate level (BSc or BS). Name Notes of vector analysis

PPSC Paper 2011 (Lecturer in Mathematics)

anonymous@undisclosed.example.com (Anonymous) — Thu, 03 Feb 2022 11:54:32 +0000

PPSC Paper 2011 (Lecturer in Mathematics) [PPSC Paper 2011 (Lecturer in Mathematics)] On this page, we have given question from old (past) paper of Lecturer in Mathematics conducted in year 2011. This is a MCQs paper and answers are given at the end of the paper. At the end of the PDF is also given to download. This paper is provided by Ms. $R$$x\in R$$x^2=x$$x^2=-x$$x^2=0$$x^2=1$$6$$8$$10$$4$$G$$H$$H$$G$$2$$4$$nZ$$Z$$n$$G$$24$$a$$a^{10}$$2$$12$$10$$V$$n$$V$$n+1$$n$$n-1$$v_1,v_2,v_3,....,v_r$$…

PPSC Paper 2015 (Lecturer in Mathematics)

anonymous@undisclosed.example.com (Anonymous) — Tue, 18 Jan 2022 10:20:00 +0000

PPSC Paper 2015 (Lecturer in Mathematics) [PPSC Paper 2011 (Lecturer in Mathematics)] On this page, we have given question from old (past) paper of Lecturer in Mathematics conducted in year 2011. This is a MCQs paper and answers are given at the end of the paper. At the end of the PDF is also given to download. This paper is provided by Kaushef Salamat. We are very thankful to her for providing this paper.$\displaystyle \int_{-4}^{0}\frac{tdt}{\sqrt{16-t62}}$$0$$-4$$4$$A\cos wt+B\sin wt$$\…

Notes of Vector Analysis (Online View)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:46:01 +0000

Notes of Vector Analysis (Online View) PDF View of Notes of the Vector Analysis is given on this page. These notes are helpful for BSc or equivalent classes. PDF file of the notes can also be downloaded from this page. Contents of these notes are available

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…

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

Report Abuse

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:39:42 +0000

Report Abuse All the resources published/posted on MathCity.org are sent by different people to help the other people for the promotion of mathematics. These are open educational resources (OER). OER are teaching, learning, and research resources that reside in the public domain or have been released under an intellectual property license that permits their free use or re-purposing by others. Open educational resources include full courses, course materials, modules, textbooks, streaming vide…

FSc Part 2 Model Papers

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:42:48 +0000

FSc Part 2 Model Papers Federal Board of Intermediate & Secondary Education, Islamabad ARW 1st Model Paper 2009 View Online Download PDF (84KB) ARW Official Model Paper (with solution) Download PDF (233KB) Board of Intermediate & Secondary Education. All the boards in Punjab expect Federal Board have the same paper pattern.

Muhammad Idrees

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:44:42 +0000

Muhammad Idrees Muhammad Idrees; M.Sc, MSC, M.Phil Department of Mathematics Govt: Boys Degree College, Nushki-Balochistan. Emails: , We are very thankful to Muhammad Idrees for contributing to the resources of MathCity.org Contribution * Exercise 3.3 |

Atiq ur Rehman, PhD

anonymous@undisclosed.example.com (Anonymous) — Sun, 01 Feb 2026 14:25:54 +0000

Atiq ur Rehman, PhD Atiq ur Rehman, PhD Associate Professor (Tenured) Department of Mathematics COMSATS University Islamabad, Attock Campus Kamra Road, Attock - PAKISTAN. Email: , Field of Research: Difference and functional equations, Real functions, Inequalities in monotonic and convex functions

Did you know?

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:39:24 +0000

Did you know? This is a new project launched by MathCity.org. The soul purpose of this project is to aware the students about those concepts of mathematics which are elementary but students don't bother to dig-deeper for those concept. Also our aim is to stimulate the mind of students to think about the core concepts of mathematics.$f(x)=x+3$$\displaystyle g(x)=\frac{x^2-9}{x-3}$$f=g$$\pi$

Report Error

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:39:27 +0000

Report Error Thank you very much for coming on this page as we understand that you come to this page for helping us and community of mathematics who are using this website. We really appreciate your effort to give us your quality time.

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.

People (Contributor)

anonymous@undisclosed.example.com (Anonymous) — Sun, 31 May 2026 07:46:52 +0000

People (Contributor) We're so grateful to all the amazing contributors on MathCity.org! This page lists all the students, teachers, and anyone who has shared their knowledge with us. Thanks to all of you, MathCity is a fantastic place to learn! *

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…

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…

Old Papers (FSc Part 2)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:42:49 +0000

Old Papers (FSc Part 2) Federal Board of Intermediate & Secondary Education, Islamabad The special page has been created for Federal Board: * Old Question Papers/Model Papers HSSC-II (FSc-II): FBISE Board of Intermediate & Secondary Education. (All the boards have same paper pattern in Punjab excluding Federal Board) These papers can be used as a model paper for other board (e.g. Multan Board, Faisalabad Board, Sargodha Board, Gujranwala Board, DG Khan Board, Rawalpindi Board etc)

Open Notes on Real Analysis I

anonymous@undisclosed.example.com (Anonymous) — Tue, 26 Aug 2025 18:16:07 +0000

Open Notes on Real Analysis I [Open Notes on Real Analysis I] This is an initial release of the notes. The beautiful thing for these notes is that you can edit these notes. If you feel that your version of notes is better than given here, we can share your version here. Please send an email to first author Dr. Atiq ur Rehman at

PPSC Paper 2021 (Lecturer in Mathematics)

anonymous@undisclosed.example.com (Anonymous) — Tue, 23 Aug 2022 17:04:49 +0000

PPSC Paper 2021 (Lecturer in Mathematics) [PPSC Paper 2011 (Lecturer in Mathematics)] On this page, we have given question from old (past) paper of Lecturer in Mathematics conducted in year 2021. This is a MCQs paper and answers are given at the end of the paper. At the end of the PDF is also given to download. This paper is provided by Ms. $2018$$4$$6$$8$$10$$X$$Y$$X\times Y$$\parallel (x,y) \parallel=\parallel x\parallel+\parallel y\parallel, \,\forall \, (x,y)\in X \times Y$\(f(…

Chapter 03: General Theorem, Intermediate Forms

anonymous@undisclosed.example.com (Anonymous) — Fri, 21 Apr 2023 13:46:07 +0000

Chapter 03: General Theorem, Intermediate Forms [BSc Calculus 3rd Chapter] What is in the this chapter? * Rolle's theorem * Geometrical interpretation of Rolle's theorem * The mean value theorems * Another form of mean value theorem * Increasing and decreasing functions$\frac{0}{0}$$\frac{\infty}{\infty}$$0\times \infty$$\infty \times 0$$\infty-\infty$$0^\infty, 1^\infty, \infty^0$

MCQs-Short Questions by Mr Parvez Khan

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:46:05 +0000

MCQs-Short Questions by Mr Parvez Khan * MCQs and Short Question written by Mr. Parvez Khan, composed by Mr. Momin Ali from Text Book of Algebra and Trigonometry Class XI (Punjab Textbook Board, Lahore) * Key to the MCQs is given at page 57. Erratum $180^{\circ}$

MCQs-Short Questions by Mr. Parvez Khan

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:46:42 +0000

MCQs-Short Questions by Mr. Parvez Khan * MCQs and Short Question by Mr. Parvez Khan composed by Momin Ali: Calculus and Analytic Geometry, MATHEMATICS 12 (Punjab Textbook Board, Lahore). Answers are given at page 32.

Targets

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:49:43 +0000

Targets Here we have listed the notes for MSc or BS Mathematics, which will be published on MathCity.org. We are working hard to find these notes. Whenever we found these notes we will put them on our website. Here are our targets. * Fluid Mechanics

Exercise 1.1 (Solutions)

anonymous@undisclosed.example.com (Anonymous) — Thu, 13 Apr 2023 09:34:48 +0000

Exercise 1.1 (Solutions) Notes (Solutions) of Exercise 1.1: Textbook of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Textbook Board (PTB) Lahore. The main topics of this exercise are properties of real numbers, binary operation, addition and multiplication law, properties of equality, properties of inequality (order properties), field, rule of fractions. These notes are based on the new Student Learning Outcomes (SLOs). Version: 4.0, Available at MathCity.org $\{0…

Exercise 2.8 (Solutions)

anonymous@undisclosed.example.com (Anonymous) — Wed, 05 Apr 2023 12:55:15 +0000

Exercise 2.8 (Solutions) Notes (Solutions) of Exercise 2.8: Textbook of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Textbook Board (PTB) Lahore. The main topic of this exercise are binary operation, semi-group, monoid, groups and abelian groups. These notes are based on the new Student Learning Outcomes (SLOs). Version: 4.1, Available at MathCity.org $\oplus$$G=\{0,1\}$\[ \begin{array}{|c|c|c|} \hline \oplus & 0 & 1 \\ \hline 0 & 1 & 1 \\ \hline 1 & 1 & …

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anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:39:27 +0000

Report Error Thank you very much for coming on this page as we understand that you come to this page for helping us and community of mathematics. We really appreciate your effort to give us your quality time. In case of “Broken Link”, please provide us the link by copying the link from address bar and paste it in comments box.

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.

MathCraft

anonymous@undisclosed.example.com (Anonymous) — Sun, 14 Apr 2024 10:56:57 +0000

MathCraft Introducing “MathCraft”: Your Solution for Document Transformation! [MathCraft] We are thrilled to unveil our latest service, MathCraft, tailored exclusively for the mathematics community. With MathCraft, you can easily get code from PDFs and pictures into LaTeX or Word files without spending too much money. Whether you're a student, researcher, or teacher, MathCraft can help you create your math documents in the format you want.

Mathematician of the day

anonymous@undisclosed.example.com (Anonymous) — Mon, 11 Mar 2024 05:54:30 +0000

Mathematician of the day The complete list of the mathematician who were born or died today is given at the following URL * It is worth mentioning that “The MacTutor History of Mathematics archive” is a database of famous mathematician and mathematics archive created by by John J O'Connor and Edmund F Robertson is available at the following

Quote of the Day

anonymous@undisclosed.example.com (Anonymous) — Thu, 25 Jul 2024 06:21:51 +0000

Quote of the Day [Quote of the Day] The “quote of the day” is a useful tool for inspiration, motivation, and self-examination It offers a daily serving of knowledge from reputable and accomplished people in a range of sectors, including literature, politics, science, and entertainment. Everyday reading and reflection on a thought-provoking quote can help people learn more, see things from other people's perspectives, and advance their personal development. Sharing the

MATH 102: Calculus II

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:40:05 +0000

MATH 102: Calculus II Course outline * Techniques of integration * Further applications of integration * Parametric equations and polar coordinates * Conic sections * Sequence and series * Power series representation of functions Assignments

MTH321: Real Analysis 1

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

MTH321: Real Analysis 1 At the end of this course the students will be able to uunderstand the basic set theoretic statements and emphasize the proofs’ development of various statements by induction. Define the limit of, a function at a value, a sequence and the Cauchy criterion. Prove various theorems about limits of sequences and functions and emphasize the proofs’ development. Define continuity of a function and uniform continuity of a function, prove various theorems about continuous func…

MTH321: Real Analysis I (Fall 2015)

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

MTH321: Real Analysis I (Fall 2015) At the end of this course the students will be able to uunderstand the basic set theoretic statements and emphasize the proofs’ development of various statements by induction. Define the limit of, a function at a value, a sequence and the Cauchy criterion. Prove various theorems about limits of sequences and functions and emphasize the proofs’ development. Define continuity of a function and uniform continuity of a function, prove various theorems about con…

MTH321: Real Analysis I (Fall 2018)

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

MTH321: Real Analysis I (Fall 2018) At the end of this course the students will be able to understand the basic set theoretic statements and emphasize the proofs’ development of various statements by induction. Define the limit of, a function at a value, a sequence and the Cauchy criterion. Prove various theorems about limits of sequences and functions and emphasize the proofs’ development. Define continuity of a function and uniform continuity of a function, prove various theorems about cont…

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,.…

MTH321: Real Analysis 1

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:40:29 +0000

MTH321: Real Analysis 1 (Spring 2015)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:40:32 +0000

MTH321: Real Analysis 1 (Spring 2015) At the end of this course the students will be able to uunderstand the basic set theoretic statements and emphasize the proofs’ development of various statements by induction. Define the limit of, a function at a value, a sequence and the Cauchy criterion. Prove various theorems about limits of sequences and functions and emphasize the proofs’ development. Define continuity of a function and uniform continuity of a function, prove various theorems about c…

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

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

Notes of Fourier Series

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:40:46 +0000

Notes of Fourier Series These notes are provided by Mr. Muhammad Ashfaq. We are really very thankful to him for providing these notes and appreciates his effort to publish these notes on MathCity.org Name Notes of Fluid Mechanics Author Qayyum Ullah Khan

1st National Conference on Pure and Applied Mathematics UoS Sargodha (04-05 May 2017)

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

1st National Conference on Pure and Applied Mathematics UoS Sargodha (04-05 May 2017) * Conference Name: 1st National Conference on Pure and Applied Mathematics * Venue: Department of Mathematics, University of Sargodha, Sargodha-PAKISTAN. *

6th World Conference on 21st Century Mathematics 2013, ASSMS, Lahore (6-9 March 2013)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:41:45 +0000

6th World Conference on 21st Century Mathematics 2013, ASSMS, Lahore (6-9 March 2013) * Conference Name: 6th World Conference on 21st Century Mathematics 2013 * Registration Deadline: December 31, 2012 * Conference Date: March 6-9, 2013 *

An Encounter of Algebra and Geometry, ASSMS, Lahore (19-22 November 2011)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:41:45 +0000

An Encounter of Algebra and Geometry, ASSMS, Lahore (19-22 November 2011) A Sharing and Learning Conference (Conference dedicated to Barbu Berceanu for his 60th birthday) * Conference Name: An Encounter of Algebra and Geometry * Registration Deadline:

2nd International Conference on Pure and Applied Mathematics UoS Sargodha (November 26-27, 2016)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:41:50 +0000

2nd International Conference on Pure and Applied Mathematics UoS Sargodha (November 26-27, 2016) * Conference Name: International Conference on Pure and Applied Mathematics * Registration Deadline: Not known ( ) * Conference Date: November 26-27, 2016

National Conference on Mathematics and Applications, UoS Sargodha (09-10 April 2018)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:41:58 +0000

National Conference on Mathematics and Applications, UoS Sargodha (09-10 April 2018) * Conference Name: 2018 National Conference on Mathematics and Applications * Venue: Department of Mathematics, University of Sargodha, Sargodha-PAKISTAN. *

One Day International Symposia on Pure and Applied Mathematics UoS Sargodha (January 27, 2014)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:42:02 +0000

One Day International Symposia on Pure and Applied Mathematics UoS Sargodha (January 27, 2014) * Conference Name: One Day International Symposium on Pure and Applied Mathematics * Registration Deadline: January 18, 2014 * Conference Date: January 27, 2014

FSc Part 1 Mathematics Notes/Solutions

anonymous@undisclosed.example.com (Anonymous) — Sun, 20 Jul 2025 09:10:04 +0000

FSc Part 1 Mathematics Notes/Solutions This is an old book. Notes of new book are available at following link: [FSc Part1 PTB Book Cover] Notes (Solutions) of Textbook of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Textbook Board (PTB) Lahore.

Mathematics 9 (Science Group)

anonymous@undisclosed.example.com (Anonymous) — Wed, 08 Mar 2023 18:04:36 +0000

Mathematics 9 (Science Group) [Mathematics 9 (Science Group)] Mathematics 9 is written by Dr. Karamat H. Dar and Prof. Irfan-ul-Haq and this book is published by Carvan Book House, Lahore, Pakistan. This book consist of 302 pages and there are 17 units. Notes of Unit 1 and 3 are provided by $ka + kb + kc$$ac + ad + bc + bd$$a^2 + 2ab + b^2$$a^2 – b^2$$a^2 + 2ab + b^2 – c^2$$a^4 + a^2b^2 + b^4$$a^4 + 4b^4$$x^2 + px + q$$ax^2 + bx + c$$(ax^2 + bx + c) (ax2 + bx + d) + k$$(x + a) (x + b) (x + c) …

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.

Advance Analysis by Ms. Iqra Liaqat

anonymous@undisclosed.example.com (Anonymous) — Fri, 21 Mar 2025 15:08:17 +0000

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 $\sigma$

Affine and Euclidean Geometry by Shahzad Idress

anonymous@undisclosed.example.com (Anonymous) — Mon, 24 Jul 2023 10:30:52 +0000

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 $R^n$

Algebra II by Syed Sheraz Asghar

anonymous@undisclosed.example.com (Anonymous) — Sun, 10 Dec 2023 14:02:42 +0000

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

Classical Mechanics by Muhammad Usman Hamid

anonymous@undisclosed.example.com (Anonymous) — Mon, 29 Jul 2024 18:38:28 +0000

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.

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$

Complex Analysis (Quick Review)

anonymous@undisclosed.example.com (Anonymous) — Wed, 26 Jun 2024 18:33:42 +0000

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$…

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.

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…

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.

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.

Fluid Mechanics I by Dr Rao Muzamal Hussain

anonymous@undisclosed.example.com (Anonymous) — Mon, 24 Jul 2023 12:45:33 +0000

Fluid Mechanics I by Dr Rao Muzamal Hussain [Fluid Mechanics I 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. These notes are based on lectures delivered by Mr. Muzammil Hussain at GC University Faisalabad.

Fluid Mechanics II by Dr Rao Muzamal Hussain

anonymous@undisclosed.example.com (Anonymous) — Tue, 29 Aug 2023 06:36:09 +0000

Fluid Mechanics II by Dr Rao Muzamal Hussain [Fluid Mechanics I 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. These notes are based on lectures delivered by Mr. Muzammil Hussain at GC University Faisalabad.

Fluid Mechanics by Muhammad Usman Hamid

anonymous@undisclosed.example.com (Anonymous) — Sun, 16 Mar 2025 12:46:08 +0000

Fluid Mechanics by Muhammad Usman Hamid [Fluid Mechanics by Muhammad Usman Hamid] We casually look around most things seem to be solids but when one thinks of the oceans, the atmosphere and on out into space it becomes rather obvious that a large portion of the earth surface and of the entire universe is in a fluid state. Therefore, it becomes essential for sciences and engineers to know something about fluid mechanics.

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$

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.

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.

Group Theory: Important Definitions and Results

anonymous@undisclosed.example.com (Anonymous) — Wed, 10 Aug 2022 15:31:46 +0000

Group Theory: Important Definitions and Results [Group Theory: 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 effort 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.$G$$a\in G$$\exists$$e\in G$$a\…

Group Theory by Mr. Muhammad Iftikhar

anonymous@undisclosed.example.com (Anonymous) — Tue, 09 Aug 2022 18:28:27 +0000

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

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…

Linear Algebra: Important Definitions and Results

anonymous@undisclosed.example.com (Anonymous) — Wed, 10 Aug 2022 16:49:49 +0000

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…

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.

Mathematical Method by Muhammad Usman Hamid

anonymous@undisclosed.example.com (Anonymous) — Mon, 17 Apr 2023 08:43:53 +0000

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…

Mathematical Statistics I by Muzammil Tanveer

anonymous@undisclosed.example.com (Anonymous) — Thu, 20 Apr 2023 16:11:58 +0000

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

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…

Mathematical Statistics by Ms. Iqra Liaqat

anonymous@undisclosed.example.com (Anonymous) — Thu, 20 Apr 2023 12:30:11 +0000

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

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$

Mechanics (Easy Notes of Mechanics)

anonymous@undisclosed.example.com (Anonymous) — Tue, 08 Aug 2023 11:46:58 +0000

Mechanics (Easy Notes of Mechanics) [Easy Notes of Mechanics] These notes are provided and prepared by Dr. Amir Mahmood. We are really very thankful to him for providing these notes and appreciates his effort to publish these notes on MathCity.org If there is error or mistake in the notes, then please directly contact to Dr. Amir Mahmood for correction. He can be accessed via his email address at

Mechanics by Sir Nouman Siddique

anonymous@undisclosed.example.com (Anonymous) — Wed, 26 Jun 2024 18:35:58 +0000

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

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.

Mechanics II (Analytic Dynamics I) by Dr Babar Ahmad

anonymous@undisclosed.example.com (Anonymous) — Sat, 24 May 2025 18:13:54 +0000

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.

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.

Multiple Choice Questions (BSc/BS/PPSC) by Akhtar Abbas

anonymous@undisclosed.example.com (Anonymous) — Sun, 24 May 2026 17:45:10 +0000

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$

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?

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)$

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

Numerical Analysis II

anonymous@undisclosed.example.com (Anonymous) — Sat, 05 Aug 2023 17:56:32 +0000

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

Operation Research by Sir Haidar Ali

anonymous@undisclosed.example.com (Anonymous) — Fri, 21 Mar 2025 17:42:28 +0000

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.

Partial Differential Equations (PDE) by M Usman Hamid

anonymous@undisclosed.example.com (Anonymous) — Sun, 09 Mar 2025 09:27:42 +0000

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

Partial Differential Equations (PDE) by Muzammil Tanveer

anonymous@undisclosed.example.com (Anonymous) — Sun, 09 Mar 2025 09:29:35 +0000

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

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…

Quantitative Reasoning II (QR2: Tools for Reasoning Skills)

anonymous@undisclosed.example.com (Anonymous) — Fri, 01 Aug 2025 18:31:56 +0000

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…

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.$\phi$

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.

Special Functions by Dr. Muhey-U-Din

anonymous@undisclosed.example.com (Anonymous) — Sun, 23 Jul 2023 16:48:30 +0000

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.

Special Theory of Relativity by M Usman Hamid and M Zeeshan Ahmad

anonymous@undisclosed.example.com (Anonymous) — Tue, 23 Aug 2022 12:32:09 +0000

Special Theory of Relativity by M Usman Hamid and M Zeeshan Ahmad [Special Theory of Relativity by M Usman Hamid and M Zeeshan Ahmad] Special theory of relativity developed by Einstein in 1905, after the failure of Newton‘s laws, when he was dealing with the relative motion in space. The theory of relativity deals with relations which exist between physical quantities (such as mass of a particle, length of a rod, electric field at a point etc.) as they appear to different observers in relative …

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.

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.

Vector Space (Review) by Rashad Wattu

anonymous@undisclosed.example.com (Anonymous) — Sat, 01 Apr 2023 14:51:01 +0000

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.

Old papers for MSc Mathematics

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:44:02 +0000

Old papers for MSc Mathematics * Previous/Past papers of University of the Punjab, Lahore and University of Sargodha. If you have any paper to share with us, you can send us a soft copy or a hard copy. Visit for more info. * University of Sargodha, Sargodha (Old Papers) Previous/Past papers of University of Sargodha, Sargodha.

M. Aftab Hanif

anonymous@undisclosed.example.com (Anonymous) — Sat, 28 Feb 2026 17:15:48 +0000

M. Aftab Hanif [M. Aftab Hanif] We would like to give a big thank you to Mr. Muhammad Aftab Hanif for his wonderful work on MathCity.org. Mr. Hanif holds an MPhil in Mathematics and is a dedicated Lecturer at Punjab College, Dhamial Campus, Rawalpindi (). His college is well-known for providing a high-quality education and helping students reach their full potential.

Muhammad Fiaz Hussain

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:44:41 +0000

Muhammad Fiaz Hussain We are very thankful to Muhammad Fiaz Hussain for contributing to our website. * M.Sc, M.Phil. in Applied & Analytic Mathematics (COMSATS Institute of Information Technology Islamabad) * Email: * Cell: +92-333-6639466; +92-300-504117

Hassan Mehboob

anonymous@undisclosed.example.com (Anonymous) — Sat, 26 Jul 2025 09:46:36 +0000

Hassan Mehboob [Mr. Raheel Ahmad] We are incredibly thankful to Mr. Hassan Mehboob for his invaluable contribution to MathCity.org. With an MPhil in Mathematics and an impressive twenty years of teaching experience, Mr. Mehboob brings a wealth of knowledge and expertise to our platform. As a Senior Subject Specialist for Mathematics, his insights are deeply rooted in practical classroom experience. He possesses a keen interest in teaching mathematics at both school and college levels, a passion …

Muzzammil Subhan

anonymous@undisclosed.example.com (Anonymous) — Sun, 20 Oct 2024 18:01:01 +0000

Muzzammil Subhan [Muzzammil Subhan] We'd like to express our deepest gratitude to Mr. Muzzammil Subhan from Narowal city! A true pioneer contributor, he's not only a fantastic teacher but also a brilliant mathematician. His contributions have been invaluable to MathCity.org, and we're so lucky to have him as part of our community.

Waseem Akram

anonymous@undisclosed.example.com (Anonymous) — Sun, 31 May 2026 07:53:55 +0000

Waseem Akram [Mr. Waseem Akram] We are very grateful to Mr. Waseem Akram for his important help with MathCity.org. He holds a bachelor’s degree in mathematics and has deep knowledge of the subject. He is especially skilled in advanced areas like functional analysis, rings, and modules. His expertise has been incredibly valuable to our community, and we truly appreciate the dedication and effort he has shared with us.

PPSC Mock Interview Lecturer Mathematics

anonymous@undisclosed.example.com (Anonymous) — Thu, 25 Mar 2021 16:31:54 +0000

PPSC Mock Interview Lecturer Mathematics [PPSC Mock Interview Lecturer Mathematics] This handout is shared by Mr. Rashad Wattu and written by Sawaira Sikandar. We are really very thankful to him for providing this handout and appreciates his efforts to publish it on MathCity.org. This handout contains the questions collected from the different interviews of the Lecturer in Mathematics conducted by Public Service Commission (PSC). This is help full to prepare interview of all types of jobs whic…

Chapter 08: Infinite Series

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:45:49 +0000

Chapter 08: Infinite Series Notes of the book Mathematical Method written by S.M. Yusuf, A. Majeed and M. Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. Infinite series are of great importance in both pure and applied mathematics. They play a significant role in Physics and engineering. In fact many functions can be represented by infinite series. The theory of infinite series is developed through the use of special kind of function called sequence.

Notes of Mechanics by Kaleem Arif

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:45:54 +0000

Notes of Mechanics by Kaleem Arif ARW Virtual Work Download PDF~3.3MB View Online bsc notes_of_bsc notes_of_mechanics_bsc

Syllabus/Model Papers for Sargodha University

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:46:03 +0000

Syllabus/Model Papers for Sargodha University Syllabus for the subjects General Mathematics, A-Course of Mathematics and B-Course of Mathematics for BSc (private and regular) from University of Sargodha, Sargodha - PAKISTAN. Every subject consists of two papers of 100 marks each. In every paper there are three sections with four questions. A student have to attempt two questions from each section. These papers are renamed from Pure and Applied Mathematics. For details, please see

MCQs by Nauman Idrees

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:46:06 +0000

MCQs Made by Nauman Idrees

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:46:08 +0000

MCQs Made by Nauman Idrees Chapter 01 View Online Download PDF (43KB) * Online View

MCQs by Nauman Idrees

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:46:43 +0000

MCQs by Nauman Idrees * Calculus and Analytic Geometry, MATHEMATICS 12 (Punjab Textbook Board, Lahore) ARW Unit 01 View Online Download PDF (48KB) Unit 01: Key ARW Unit 02 View Online Download PDF (62KB) Unit 02: Key ARW Unit 03 View Online Download PDF (72KB) Unit 03: Key ARW Unit 04 View Online Download PDF (48KB) Unit 04: Key ARW Unit 05 View Online Download PDF (52KB) Unit 05: Key ARW

Normed Spaces: Short Questions and MCQs

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:48:16 +0000

Normed Spaces: Short Questions and MCQs

Number Theory by Ms. Iqra Liaqat

anonymous@undisclosed.example.com (Anonymous) — Tue, 11 May 2021 11:51:22 +0000

Number Theory by Ms. Iqra Liaqat [Number Theory by Ms. Iqra Liaqat] Notes of number theory provided Ms. Iqra Liaqat is a very good addition in the MSc notes section. We are actually quite grateful to her for giving these notes and likes her encouragement to distribute these notes on MathCity.org Name

Syllabus for PU

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

Syllabus for PU Syllabus and scheme of studies for Regular/Private students doing MSc Mathematics from University of the Punjab, Lahore. 2 years M.Sc Mathematics programme consists of two parts namely Part-I and Part II. The regulation, Syllabi and Courses of Reading for the M.Sc. (Mathematics) Part-I and Part-II (Regular Scheme) are given below.

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

University of Sargodha (Old Papers): BSc (Mathematics only)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:50:33 +0000

University of Sargodha (Old Papers): BSc (Mathematics only) Old/previous papers of BSc (Mathematics), University of Sargodha, Sargodha are posted on this page. There are three type of papers in BSc: General Mathematics, A-Course of Mathematics and B-Course of Mathematics. The A-Course of Mathematics is renamed from

University of the Punjab, Lahore (Old Papers)

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:50:42 +0000

University of the Punjab, Lahore (Old Papers) Old papers for MSc (Mathematics), University of the Punjab, Lahore. Hopefully this will help students to understand the pattern. . Notes of different subject are available in MSc Notes section of this website.

University of Sargodha, Sargodha (Old Papers)

anonymous@undisclosed.example.com (Anonymous) — Thu, 28 Mar 2024 16:26:23 +0000

University of Sargodha, Sargodha (Old Papers) * To open or print a DjVu file, you must have some DjVu file viewer, e.g. WinDjVu. It can be downloaded from here * From 1st Annual 2013, the paper pattern has been changed. Check the complete syllabus

Chapter 03: PDF Viewer

anonymous@undisclosed.example.com (Anonymous) — Sun, 07 Feb 2021 16:51:57 +0000

Chapter 03: PDF Viewer Notes of the Chapter 03: General Theorem, Intermediate Forms with Analytic Geometry written by Dr. S. M. Yusuf and Prof. Muhammad Amin, published by Ilmi Kitab Khana, Lahore - PAKISTAN. There are three exercises in this chapter.

Exercise 1.2 (Solutions)

anonymous@undisclosed.example.com (Anonymous) — Sun, 09 Apr 2023 07:32:53 +0000

Exercise 1.2 (Solutions) Notes (Solutions) of Exercise 1.2: Textbook of Algebra and Trigonometry Class XI (Mathematics FSc Part 1 or HSSC-I), Punjab Textbook Board (PTB) Lahore. The main topics of this exercise are complex numbers, real part and imaginary part of complex numbers, properties of the fundamental operation on complex numbers, complex number as ordered pair of real numbers and special subset of complex numbers. These notes are based on the new Student Learning Outcomes (SLOs). Versio…

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 $z= f(x,y)$