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- MTH321: Real Analysis I (Spring 2020)
- ize the proofs’ development of various statements by induction. Define the limit of, a function at a v... cleanly. The first rigorous definition was given by Georg Cantor in 1871. * In the 16th century, Si... 11- Define convergence of the sequence. * 2.12- By definition, prove that $\lim\limits_{n\to\infty}\frac{2n}{n+2}=2$. * 2.13- By definition, prove that $\lim\limits_{n\to\infty}\
- MTH321: Real Analysis I (Fall 2021)
- ize the proofs’ development of various statements by induction. Define the limit of, a function at a v... cleanly. The first rigorous definition was given by Georg Cantor in 1871. * In the 16th century, Si... 11- Define convergence of the sequence. * 2.12- By definition, prove that $\lim\limits_{n\to\infty}\frac{2n}{n+2}=2$. * 2.13- By definition, prove that $\lim\limits_{n\to\infty}\
- MTH424: Convex Analysis (Fall 2020)
- ndependent and enhance their mathematical ability by giving them home work and projects. ===== Course... ion * Example of convex & concave functions * By definition, prove that $f(x)=x$ is convex on $\mathbb{R}$. * By definition, prove that $f(x)=x^2$ is convex on $\... \mathbb{R}$ is convex, then $f$ is bounded above by $\max(f(a),f(b))$. ===Lecture 03=== * Defini
- MTH321: Real Analysis I (Fall 2019)
- x.jpg?nolink|Photo-illustration of Zeno's Paradox by Juliana Jiménez Jaramillo. Photo by Twildlife/Thinkstock}} At the end of this course the students wi... ize the proofs’ development of various statements by induction. Define the limit of, a function at a v... cleanly. The first rigorous definition was given by Georg Cantor in 1871. * In the 16th century, Si
- MTH604: Fixed Point Theory and Applications (Spring 2020)
- eorem. - Find the fixed point of $f(x)=2x-2x^2$ by iteration method by taking initial guess $x_0=0.1$. - Define metric spaces, open ball, closed ball,... usual metric and $T:X\to X$ be a mapping defined by $T(x)=\frac{10}{11}\left(x+\frac{1}{x} \right)$ f... usual metric and $T:X\to X$ be a mapping defined by $T(x)=\frac{1}{7}(x^3+x^2+1)$ for all $x\in X$. P
- MTH633: Advanced Convex Analysis (Spring 2017)
- ==== Recommended books: ===== * Convex Analysis by R. Tyrrell Rockafellar. * Convex Analysis By Jan van Tiel. * Analysis: Convex Analysis and approximation theoryby R. V. Gamkrelidze, Sergeĭ Mikhaĭlovich Nikolskiĭ. * Abstract convex Analysis by Ivan Singer. * [[https://books.google.com.pk/bo
- MTH633: Advanced Convex Analysis (Spring 2019)
- ==== Recommended books: ===== * Convex Analysis by R. Tyrrell Rockafellar. * Convex Analysis By Jan van Tiel. * Analysis: Convex Analysis and approximation theoryby R. V. Gamkrelidze, Sergeĭ Mikhaĭlovich Nikolskiĭ. * Abstract convex Analysis by Ivan Singer. * [[https://books.google.com.pk/bo
- MTH321: Real Analysis I (Spring 2023)
- ize the proofs’ development of various statements by induction. Define the limit of, a function at a v... cleanly. The first rigorous definition was given by Georg Cantor in 1871. * In the 16th century, Si... of $\mathbb{N}$ such that $\sup E = \inf E$. - By defintion, prove that $0$ is even number. - Pro... s/CalcI/DefnOfLimit.aspx (find limit of functions by definition) * Seidel, Paul. 18.100C Real Analys
- MTH424: Convex Analysis
- ndependent and enhance their mathematical ability by giving them home work and projects. ===== Course... r Programming Theory and Algorithms, 3rd Edition, by M. S. Bazaraa, H. D. Sherali and C. M. Shetty. ... and Their Applications, A Contemporary Approach, by C. P. Niculescu and L. E. Persson. - Convex Analysis and Monotone Operator Theory in Hilbert Spaces, by H. H. Bauschke and P. L. Combettes.
- MTH321: Real Analysis I (Fall 2015)
- ize the proofs’ development of various statements by induction. Define the limit of, a function at a v... cleanly. The first rigorous definition was given by Georg Cantor in 1871. * In the 16th century, Si... s/CalcI/DefnOfLimit.aspx (find limit of functions by definition) * Seidel, Paul. 18.100C Real Analys... hematics/18-100c-real-analysis-fall-2012 (Accessed 29 Apr, 2014). License: Creative Commons BY-NC-SA
- MTH321: Real Analysis I (Fall 2018)
- ize the proofs’ development of various statements by induction. Define the limit of, a function at a v... cleanly. The first rigorous definition was given by Georg Cantor in 1871. * In the 16th century, Si... s/CalcI/DefnOfLimit.aspx (find limit of functions by definition) * Seidel, Paul. 18.100C Real Analys... Accessed 29 Apr, 2014). License: Creative Commons BY-NC-SA =====Recommended book ===== - Rudin, W.
- MTH321: Real Analysis I (Fall 2022)
- ize the proofs’ development of various statements by induction. Define the limit of, a function at a v... cleanly. The first rigorous definition was given by Georg Cantor in 1871. * In the 16th century, Si... s/CalcI/DefnOfLimit.aspx (find limit of functions by definition) * Seidel, Paul. 18.100C Real Analys... Accessed 29 Apr, 2014). License: Creative Commons BY-NC-SA =====Recommended book ===== - Rudin, W.
- MTH633: Advanced Convex Analysis
- ==== Recommended books: ===== * Convex Analysis by R. Tyrrell Rockafellar. * Convex Analysis By Jan van Tiel. * Analysis: Convex Analysis and approximation theoryby R. V. Gamkrelidze, Sergeĭ Mikhaĭlovich Nikolskiĭ. * Abstract convex Analysis by Ivan Singer.
- MTH633: Advanced Convex Analysis (Spring 2015)
- ==== Recommended books: ===== * Convex Analysis by R. Tyrrell Rockafellar. * Convex Analysis By Jan van Tiel. * Analysis: Convex Analysis and approximation theoryby R. V. Gamkrelidze, Sergeĭ Mikhaĭlovich Nikolskiĭ. * Abstract convex Analysis by Ivan Singer.
- MTH424: Convex Analysis (Spring 2024)
- ndependent and enhance their mathematical ability by giving them home work and projects. ===== Course... r Programming Theory and Algorithms, 3rd Edition, by M. S. Bazaraa, H. D. Sherali and C. M. Shetty. ... and Their Applications, A Contemporary Approach, by C. P. Niculescu and L. E. Persson. - Convex Analysis and Monotone Operator Theory in Hilbert Spaces, by H. H. Bauschke and P. L. Combettes.