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Khuram Ali Khan
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y.org>\\ \\ **Field of Research:** Difference and functional equations, Real functions, Mathematical inequalities involving convex functions, Time Scales Calculus, Soft Sets </WRAP> <W... Discrete Jensen's Inequality for Operator Convex Functions, J. Math. Comput. Sci., vol. 2 (2012), No.
Definitions: FSc Part 2 (Mathematics): PTB @fsc-part2-ptb
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** for his valuable contribution. ===== Unit 01 (Functions and Limits) ===== * **Function:** A function is a rule or correspondence, relating to two sets in such a way that each element i... e and only one element in the second set. Or \\ A function from //X// to //Y// is a rule that assigns t
Atiq ur Rehman, PhD
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tk.edu.pk> **Field of Research:** Difference and functional equations, Real functions, Inequalities in monotonic and convex functions * See profile at [[https://mathscinet.ams.org... of Hadamard type for exponentially (s, m)-convex functions, AIMS Mathematics, 6(1) (2021), 882–892. 5
Unit 01: Functions and Limits @fsc:fsc_part_2_solutions
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====== Unit 01: Functions and Limits ====== {{ :fsc:fsc_part_2_solutions:fsc-2-unit-01-ptb.jpg?nolink|Unit 01: Functions and Limits}} Notes (Solutions) of Unit 01: Functions and Limits, Calculus and Analytic Geometry,... & summary ==== * Introduction * Concept of Function * Definition (Function-Domain-Range)
FSc Part 2 (KPK Boards) @fsc
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: | PDF Scanned (Handwritten) | ===== Unit 01: Functions and Limits ===== {{ :fsc:kpk_fsc_part_2:kpk... e able to: * identify the domain and range of a functions through graphs. * draw the graph of modulus function and identify its domain and range. * recognize the composition of a function and then to find out the composition of two
MTH322: Real Analysis II (Fall 2021) @atiq
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]]. ===== Course Contents: ===== **Sequences of functions:** convergence, uniform convergence, unifor... differentiation, the exponential and logarithmic function, the trigonometric functions. **Series of functions:** Absolute convergence, uniform convergence, Cauchy criterion, Weiestra
Special Functions by Dr. Muhey-U-Din @notes
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====== Special Functions by Dr. Muhey-U-Din ====== These notes are provided and composed by Mr. [[:peo... the lectures by Dr. Muhey-U-Din. {{ notes:special-functions-muzammil-tanveer.jpg?nolink|Special Functions}} ^ Name |Special Functions | ^ Provider |Mr. Muzammil Tanveer | ^Lectured by |Dr. Muhey-U-
MCQs: Ch 02 Sets, Functions and Groups @fsc-part1-ptb:mcq-bank
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====== MCQs: Ch 02 Sets, Functions and Groups ====== High quality MCQs of Chapter 02 Sets, Functions and Groups of Text Book of Algebra and Trig... objects is called - Relation - Sets - Function - None of these - The objects in a set... \sim p \wedge \sim q$ - Every relation is - Function - Cartesian product - May or may not
MTH424: Convex Analysis (Fall 2020) @atiq
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e concept of Convex Analysis, convex sets, convex functions, Differential of the convex function. Developing ability to study the Hadamard-Hermite inequalit... ir properties, Best approximation theorem. Convex functions, Basic definitions, properties, various generalizations, Differentiable convex functions, Hermite and Hadamard inequalities, Subgrad
MTH322: Real Analysis II (Spring 2023) @atiq
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]]. ===== Course Contents: ===== **Sequences of functions:** Convergence, uniform convergence, unifor... differentiation, the exponential and logarithmic function, the trigonometric functions. **Series of functions:** Absolute convergence, uniform convergence, Cauchy criterion, Weiestra
Definitions: FSc Part 1 (Mathematics): PTB @fsc-part1-ptb
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by $|x+iy|$ or $|(x,y)|$. ===== Chapter 02: Functions and groups ===== * **Set:** A set is gene... w q)\wedge (p \vee q)$ is the contingency. * **Function:** Let $A$ and $B$ be two non-empty set sets... $F$ have same 1st elements. Then $F$ is called a function from $A$ to $B$ and is written as $F:A \to B$ denoted by $y=f(x)$. * **Bijective function:** (1-1 and onto) A function f which is bot
Definitions: FSc Part 1 (Mathematics): PTB by Aurang Zaib @fsc-part1-ptb
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of \( p \) and \( q \) and false for others. ====Function==== A function is a relation between two non-empty sets \( A \) and \( B \), where each element o... ( A = \{1, 2, 3\} \) and \( B = \{a, b, c\} \). A function \( f: A \rightarrow B \) could be defined as... ( f(1) = a, f(2) = b, f(3) = c \). ====Bijective Function==== A bijective function is a function that
FSc Part 1 (KPK Boards) @fsc
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presentation of a vector in a space. * know the fundamental defintion of vector using geometrical as ... * define unit vectors i, j and k. * repeat all fundamental definitions of vector in plane for space.... first n natural numbers by n!. * recognize the fundamental principle of counting and its illustratio... orem|Online view]]** </callout> ===== Chapter 8: Functions and Graphs ===== === Objectives === After r
Are the functions are same? @dyk
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====== Are the functions are same? ====== {{ :dyk:are_the_functions_are_same.jpg?direct |Are the functions are same?}} Consider two functions $f(x)=x+3$ and $\displaystyle g(x)=\frac{x^2-9}{x-3}$. Is $f
Advanced Analysis: Handwritten Notes @notes
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retation of Equivalent Set * Duality * Choice Function * Characteristic Function * Cardinal Numbers * Arithmetic Cardinal Number * Transfinite C... ial Equation * Hyper-geometric Series * Gamma Function * Beta Function * Relation between Gama and Beta Function * Bessel Function * Differenti
MTH321: Real Analysis I (Spring 2023) @atiq
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Mathematical Method by Sir Muhammad Awais Aun @notes
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Measure Theory Notes by Anwar Khan @notes
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Functional Analysis by Mr. Tahir Hussain Jaffery @notes
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Notes of Analysis @notes
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PPSC Paper 2021 (Lecturer in Mathematics) @ppsc
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MTH321: Real Analysis I (Fall 2018) @atiq
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MTH321: Real Analysis I (Fall 2019) @atiq
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MTH321: Real Analysis I (Fall 2021) @atiq
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MTH321: Real Analysis I (Fall 2022) @atiq
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MTH103: Exploring Quantitative Skills @atiq
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MTH321: Real Analysis I (Spring 2020) @atiq
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Handwritten Notes of Real Analysis by Asim Marwat @notes
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MTH321: Real Analysis I (Fall 2015) @atiq
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Functional Analysis by Prof Mumtaz Ahmad @notes
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Real Analysis Handwritten Notes by Kaushef Salamat @notes
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Unit 02: Differentiation @fsc:fsc_part_2_solutions
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Notes of Mathematics
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MTH321: Real Analysis 1 @atiq
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MATH-731: Convex Analysis @atiq
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MTH321: Real Analysis 1 @atiq
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MTH321: Real Analysis 1 (Spring 2015) @atiq
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Advance Analysis by Ms. Iqra Liaqat @notes
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MTH322: Real Analysis II (Fall 2016) @atiq
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MTH322: Real Analysis II (Fall 2017) @atiq
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MTH322: Real Analysis II (Spring 2017) @atiq
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MathCraft: PDF to LaTeX file: Sample-01 @mathcraft
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MTH424: Convex Analysis @atiq
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MTH322: Real Analysis II (Fall 2018) @atiq
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MTH322: Real Analysis II (Fall 2020) @atiq
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MATH-301: Complex Analysis @atiq
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MTH322: Real Analysis II (Spring 2019) @atiq
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MTH322: Real Analysis II (Spring 2022) @atiq
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MTH424: Convex Analysis (Spring 2024) @atiq
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Measure Theory Handwritten Notes by Asim Marwat @notes
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MTH322: Real Analysis II (Fall 2019) @atiq
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MTH322: Real Analysis II (Spring 2016) @atiq
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MTH604: Fixed Point Theory and Applications @atiq
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Notes of Vector Analysis @bsc
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Definitions: FSc Part1 KPK @fsc-part1-kpk
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Definitions: FSc Part1 KPK @math-11-kpk
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Measure Theory by M Usman Hamid & Saima Akram @notes
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MTH211: Discrete Mathematics (Fall 2020) @atiq
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MATH-505: Complex Analysis @atiq
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Mathematical Statistics by Ms. Iqra Liaqat @notes
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PPSC Paper 2011 (Lecturer in Mathematics) @ppsc
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Question 1, Exercise 10.1 @fsc-part1-kpk:sol:unit10
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Question 1, Exercise 10.1 @math-11-kpk:sol:unit10
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MTH322: Real Analysis II (Fall 2015) @atiq
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MATH-305: Real Analysis-I @atiq
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MTH211: Discrete Mathematics (Spring 2020) @atiq
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MTH211: Discrete Mathematics (Fall 2020) @atiq
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MTH211: Discrete Mathematics (Spring 2022) @atiq
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Mathematical Method by Muhammad Usman Hamid @notes
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Partial Differential Equations by Muzammil Tanveer @notes
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Real Analysis Notes by Prof Syed Gul Shah @notes
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MCQs with key @fsc:fsc_part_2_mcqs
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Chapter 08: Function and Graphs @fsc:kpk_fsc_part_1
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Preparation Guide @msc:syllabus:uos
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MTH611: Integral Inequalities (Fall 2019) @atiq
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MATH-300: Basic Mathematics for Chemist @atiq
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Notes of Fourier Series @bsc
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Vector Analysis by Hameed Ullah: Notes @bsc
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Important Questions: HSSC-I @fsc-part1-ptb
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Complex Analysis by M Usman Hamid @notes
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Number Theory: Handwritten Notes @notes
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Theory of Optimization by Ma'am Iqra Razzaq @notes
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Nawab Ali @people
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MCQs: Ch 04 Quadratic Equations @fsc-part1-ptb:mcq-bank
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CHEM-501: Basic Mathematics for Chemist @atiq
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MATH 103: Number Theory @atiq
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General Mathematics 9 @matric
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Complex Analysis (Notes) by Ms. Iqra Liaqat @notes
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Differential Geometry by Syed Hassan Waqas @notes
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Mathematical Statistics II by Sir Haidar Ali @notes
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Topology: Handwritten Notes @notes
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Unit 03: Vectors (Solutions) @math-11-kpk:sol
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Syllabus for PU @msc:syllabus
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Question 7 and 8 Exercise 6.2 @math-11-kpk:sol:unit06
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Mathematics CUI: LaTeX Resources
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MTH604: Fixed Point Theory and Applications @atiq
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MTH480: Introductory Quantum Mechanics @atiq
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MATH-510: Topology @atiq
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MATH-510: Topology @atiq
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MTH633: Advanced Convex Analysis @atiq
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MTH633: Advanced Convex Analysis (Spring 2015) @atiq
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MTH633: Advanced Convex Analysis (Spring 2017) @atiq
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MTH633: Advanced Convex Analysis (Spring 2019) @atiq
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Some important series of functions @bsc
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Mathematics 10 (Science Group) @matric
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Fluid Dynamics I by Muhammad Usman Hamid @notes
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General Topology by Azhar Hussain @notes
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Mathematical Statistics I by Muzammil Tanveer @notes
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Number Theory Notes by Anwar Khan @notes
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Operation Research by Sir Haidar Ali @notes
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Rings (Handwritten notes) @notes
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Vector Spaces (Handwritten notes) @notes
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Matric 9th (General): Online View @matric:9th_general
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Number Theory by Ms. Iqra Liaqat @msc:notes
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Question 3 and 4 Exercise 6.2 @math-11-kpk:sol:unit06
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Question 11 Exercise 6.2 @math-11-kpk:sol:unit06
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About Us
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Did you know?
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PPSC General Information, Syllabus, Paper Pattern
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Software
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MATH 102: Calculus II @atiq
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Notes of Calculus with Analytic Geometry @bsc
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Notes of Metric Spaces @bsc
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Notes of Metric Spaces by Umer Asghar @bsc
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Number Theory by Prof. Asghar Ali @bsc
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Solution and Area of Oblique Triangle @fsc-part1-ptb
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Trigonometric Formulas @fsc-part1-ptb
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Important Questions: HSSC-II @fsc-part2-ptb
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Trigonometric Review @fsc
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MathCraft: PDF to LaTeX file: Sample-02 @mathcraft
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Complex Analysis (Quick Review) @notes
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Fluid Mechanics by Ali Raza @notes
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Fluid Mechanics I by Dr Rao Muzamal Hussain @notes
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General Topology by Raheel Ahmad @notes
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Number Theory by Dr Muhammad Umer Shuaib @notes
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Operation Research: Handwritten Notes @notes
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Partial Differential Equations by M Usman Hamid @notes
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Ring (Notes) by Prof. M. Dabeer Mughal @notes
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Rings & Modules by Ms. Iqra Liaqat @notes
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Vector Space (Review) by Rashad Wattu @notes
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Akhtar Abbas @people
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Amir Shehzad @people
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Asim Marwat @people
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PPSC Paper 2015 (Lecturer in Mathematics) @ppsc
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PPSC Mock Interview Lecturer Mathematics @ppsc
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Quotes for the April @quote-of-the-day
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Quotes for the May @quote-of-the-day
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Formatting Syntax @wiki
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Welcome to your new DokuWiki @wiki
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What is Mathematics? @atiq:math-608
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MCQs or Short Questions @atiq:sp15-mth321
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Chapter 01: Number System @fsc:fsc_part_1_solutions
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Chapter 04: Quadratic Equations @fsc:fsc_part_1_solutions
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Assessment Scheme @fsc:fsc_part_2_model_papers
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Unit 03: Integration @fsc:fsc_part_2_solutions
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Targets @msc:notes
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Syllabus for UoS (Private only) @msc:syllabus
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Exercise 1.2 (Solutions) @fsc-part1-ptb:sol:ch01
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Question 5 and 6 Exercise 6.2 @math-11-kpk:sol:unit06
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Question 9 Exercise 6.3 @math-11-kpk:sol:unit06
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Question 7 & 8 Review Exercise 6 @math-11-kpk:sol:unit06
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Question 8 and 9, Exercise 10.2 @math-11-kpk:sol:unit10
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