# Notes of Mathematics

Mathematics is a language of science and is a basic need for physical or natural sciences as well as social sciences. On this page, notes on different subjects related to mathematics are listed. These notes or resources might be helpful for ADS or BS or MSc or MPhil Mathematics. These notes are send by different students or teachers. We are very thankful to them for sending us these notes. These notes are provided as it is as open educational resources with out any warranty. Please take care while using these notes and its better to use books as reference instead of these notes.

## 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 Muhammad Usman Hamid

**Group Theory by Mr. Muhammad Iftikhar**

A well written notes of groups theory for students of BS or MSc. Best to prepare a Group section of Algebra paper in MSc.

**Groups (Handwritten Notes)**

A handwritten notes of groups, usually teaches in universities. Best to prepare a Group section of Algebra paper in MSc.

**Group Theory: Important Definitions and Results**

This collections is made and shared by Akhtar Abbas. These important definitions with examples and results (theorems) may be useful to prepare interviews, PPSC, FPSC or any other examinations after MSc.

**Linear Algebra: Important Definitions and Results**

This collections is made and shared by Akhtar Abbas. These important definitions with examples and results (theorems) may be useful to prepare interviews, PPSC, FPSC or any other examinations after MSc.

**Ring (Notes) by Prof. M. Dabeer Mughal**

A handwritten notes of Ring (Algebra) by Prof. M. Dabeer Mughal (Federal Directorate of Education, Islamabad, PAKISTAN). Best to prepare a “Rings & Vector Spaces” section of Algebra paper or Algebra II for BS or MS Mathematics.

**Rings (Handwritten notes)**

A handwritten notes of rings, usually teaches in Pakistani universities. Best to prepare a Rings section of Algebra paper in MSc (Mathematics).

**Rings & Modules by Ms. Iqra Liaqat**

A handwritten notes of rings and modules, usually teaches in Pakistani universities at BS & MSc level. Best to prepare the paper of Rings and Modules at BS or MSc (Mathematics).

## Analysis

**Advanced Analysis: Handwritten Notes**

A handwritten notes of Advanced Analysis provided by Mr. Anwar Khan. We are really very thankful to Mr. Anwar Khan for providing these notes of 260 pages.

**Advance Analysis by Ms. Iqra Liaqat**

A handwritten notes of Advanced Analysis provided by Ms. Iqra Liaqat. Summary and contents are given on the page of notes.

**Complex Analysis (Easy Notes of Complex Analysis)**

An easy notes of complex analysis prepared by Mr. Haider Ali and supervised by Dr. Amir Mahmood.

**Complex Analysis by M Usman Hamid**

These notes covers most of the complex analysis.

**Complex Analysis (Notes) by Ms. Iqra Liaqat**

Handwritten notes of complex analysis by Iqra Liaqat.

**Complex Analysis (Quick Review)**

A quick review of the complex analysis by Akhtar Abbas. It may be useful to prepare interviews, PPSC, FPSC or any other examinations after MSc.

**Functional Analysis by M Usman Hamid and Zeeshan Ahmad**

These notes are written by Muhammad Usman Hamid and Zeeshan Ahmad. These are comprehensive notes covering most of the topics.

**Functional Analysis by Mr. Tahir Hussain Jaffery**

Notes of functional analysis written by Tahir Hussain Jaffery of Peshawar University, Peshawar.

**Functional Analysis by Prof Mumtaz Ahmad**

Notes of functional analysis by Prof. Mumtaz Ahmad. These notes are collected by Muhammad Saleem, composed and send by Muzammil Tanveer

**Fundamental of Complex Analysis (Solutions of Some Exercises)**

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.

**Handwritten Notes of Real Analysis by Asim Marwat**

These notes are send and written by Asim Marwat. We are very thankful to him for sharing these notes.

**Real Analysis Notes by Prof Syed Gul Shah**

Notes by Syed Gul Shah (Ex Chairman, University of Sargodha, Sargodha. Pakistan).

**Real Analysis Handwritten Notes by Kaushef Salamat**

Handwritten notes of Real Analysis by Ms. Kaushef Salamat. These are covering almost all the contents of the real analysis.

## Differential Equations

**Partial Differential Equations by M Usman Hamid**

Notes of Partial Differential Equations by Muhammad Usman Hamid. These notes 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.

**Partial Differential Equations**

Notes of Partial Differential Equations by Muzammil Tanveer. We are very thankful to him for sharing these notes.

## Differential Geometry

**Affine and Euclidean Geometry by Shahzad Idress**

Short notes by shahzad-idress. These are very useful for BS or MSc mathematics.

**Differential Geometry: Handwritten Notes**

A handwritten notes of Differential Geometry of Three Dimensions by Prof. (Rtd) Muhammad Saleem. Best to prepare a “Differential Geometry” section of Complex Analysis paper in MSc (Mathematics).

**Differential Geometry by M Usman Hamid**

A notes of Differential Geometry composed by Muhammad Usman Hamid. It covers one the section of the paper of complex analysis and in semester system it is taught as complete subject.

**Differential Geometry by Syed Hassan Waqas**

A notes of Differential Geometry composed by Mr. Muzammil Tanveer. We are very thankful to him for sending these notes.

**Differential Geometry (Notes) by Ms. Kaushef Salamat**

A notes of Differential Geometry send by Kaushef Salamat. We are very thankful to her for sending these notes.

**Differential Geometry by M Usman Hamid**

A notes of Differential Geometry composed by Muhammad Usman Hamid. It covers one the section of the paper of complex analysis and in semester system it is taught as complete subject.

## Fluid Mechanics

**Fluid Dynamics I by Muhammad Usman Hamid**

A notes of Fluid Dynamics I written by Muhammad Usman Hamid. We are very thankful to him for sending these notes.

**Fluid Mechanics I by Dr Rao Muzamal Hussain**

These notes are composed by Mr. Muzammil Tanveer, we are very thankful to him for sending these notes.

**Mechanics I (Statics) by Dr Babar Ahmad**

Book of Mechanics I (Statics) shared by Dr Babar Ahmad, the author of the book. We are very thankful to him for sharing his book for the students/teachers.

## Mathematical Method

Notes of Mathematical Method by Sir Muhammad Awais Aun compiled by Mr. Muzammil Tanveer.

Notes of Mathematical Method by Muhammad Usman Hamid. These notes are useful for BS.

## Mathematical Statistics

Handwritten notes Mathematical Statistics send by Ms. Iqra Liaqat.

Notes of Mathematical Statistics complied by Mr. Muzammil Tanveer

Notes of Mathematical Statistics II complied by Mr. Muzammil Tanveer base on the lectures by Sir Haider Ali.

## Measure Theory

Handwritten notes of measure theory by Asim Marwat. These notes cover topics ranging from the fundamentals, such as equivalence sets, to the advanced, such as convergent in measure.

## Mechanics

**Mechanics (Easy Notes of Mechanics)**

These notes are provided by Dr. Amir Mahmood.

**Mechanics by Sir Nouman Siddique**

Notes of Mechanics by Sir Nouman Siddique. These notes are collected by Muhammad Saleem, composed and send by Muzammil Tanveer

**Mechanics I (Statics) by Dr Babar Ahmad**

Book of Mechanics I (Statics) shared by Dr Babar Ahmad, the author of the book. We are very thankful to him for sharing his book for the students/teachers.

## Metric Space & Topology

**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. These are actually based on the lectures delivered by Prof. Muhammad Ashfaq (Ex HoD, Department of Mathematics, Government College Sargodha).

**Topology and Functional Analysis Solved Paper by Noman Khalid**

Solved paper of Topology and Functional Analysis offered by the University of the Punjab, Lahore.

**Topology: Handwritten Notes**

Handwritten notes of topology by Tahir Mehmmod. These notes covers almost every topic of the syllabus of paper Topology for MSc Mathematics.

**Topology Notes by Azhar Hussain**

Lecture Notes on Topology by Azhar Hussain.

**General Topology by Raheel Ahmad**

Notes of general topology. These are handwritten notes by Mr Raheel Ahmad.

## Number Theory

**Number Theory: Handwritten Notes**

A handwritten notes of Number Theory. This consist of two parts. These notes are very helpful to prepare one of the optional papers of MSc (Mathematics).

**Number Theory: Notes by Anwar Khan**

A handwritten notes of Number Theory by Mr. Anwar Khan. These notes also inclue algebraic number theory section. These notes are very helpful to prepare one of the optional papers of MSc (Mathematics).

**Number Theory by Dr Muhammad Umer Shuaib**

Notes of number theory lectured by Sir Muhammad Umer Shuaib compiled by Muzammil Tanveer.

## Numerical Analysis

**Numerical Analysis by M Usman Hamid**

A notes of numerical analysis by Muhammad Usman Hamid. In most of the universities this course is considered as compulsory.

**Numerical Analysis II**

These notes are send my Mr. Muzammil Tanveer. We are very thankful to him for sharing these notes.

## Operational Research

**Operation Research by Sir Haidar Ali**

Notes of operation research complied by Mr Muzammil Tanveer. These are based on lecture by Sir Haidar Ali at GC University, Faisalabad.

**Operation Research: Handwritten Notes**

A handwritten notes of Operation Research. These notes are very helpful to prepare one of the optional papers of MSc (Mathematics).

## Vector & Tensor Analysis

**Vector & Tensor Analysis by Prof Fazal Abbas**

Solutions of chpater 6 of a book “Vector & Tensor Analysis” by Dr. Nawazish Ali Shah written by Prof. Fazal Abbas Sajid

**Vector & Tensor Analysis by Dr Nawazish Ali (Solutions)**

Handwritten solutions of chapters 5 and 6 of the book Vector & Tensor Analysis by Dr. Nawazish Ali Shah provided by Prof. Fazal Abbas Sajid

**Vector Spaces (Handwritten notes)**

A handwritten notes of vector spaces based on the lecture of Prof. Dr. Muhammad Khalid Mehmood. These are basic notes to understand the concept of vector space.

**Vector Space (Review) by Rashad Wattu**

A review notes of Vector Space written by Hadiqa Mumtaz based on lectures delivered by Mr. Rashad Wattu.

## Other Notes

**Computing Tools for Mathematics by Asif Arshad**

These notes contain codes and techniques to work on famous software Mathematica.

**Fuzzy Sets Theory by Umar Saeed Bunarai**

Handwritten notes send by Mr. Umar Saeed Bunarai. These notes are helpful for the students of BS and MSc mathematics.

**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 send and written by Muhammad Usman Hamid.

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

These are very useful notes consists of MCQs of different subjects, which can be helpful for BSc, BS or PPSC.

**Special Functions by Dr. Muhey-U-Din**

Notes of special functions by Mr Muzammil Tanveer. These are based on lecture by Dr. Muhey-U-Din at GC University, Faisalabad.

**Theory of Optimization by Ma'am Iqra Razzaq**

Notes of Optimization Theory written by Mr Muzammil Tanveer based on lectures by Ma’am Iqra Razzaq.

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

Notes of Special Theory of Relativity written by Mr Muhammad Usman Hamid and Muhammad Zeeshan Ahmad.

**Theory of Relativity & Analytic Dynamics: Handwritten Notes**

Handwritten notes by Prof.(Rtd) Asmat Ullah, Government College, Sargodha. These notes cover most of the analytic dynamics section.