MathCity.org

CSC456: Stochastic Processes (Spring 2026)

admin@undisclosed.example.com (Administrator) — Wed, 03 Jun 2026 08:38:47 +0000

CSC456: Stochastic Processes (Spring 2026) [Stochastic Processes (Spring 2026), Image Courtesy: Gemini] Course Learning Outcomes: * To define basic concepts from the theory of Markov chains and present proofs for the most important theorems. * To compute probabilities of transition between states and return to the initial state after long time intervals in Markov chains.

Participate

admin@undisclosed.example.com (Administrator) — 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.

Waseem Akram

admin@undisclosed.example.com (Administrator) — 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.

waseem-akram.webp

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Advance Functional Analysis by Waseem Akram - [Notes of other subjects]

admin@undisclosed.example.com (Administrator) — Sun, 31 May 2026 07:51:28 +0000

Advance Functional Analysis by Waseem Akram [Advance Functional Analysis by Waseem Akram] These notes provide a concise yet dense overview of key theorems in functional analysis, including the Hahn-Banach Theorem, Baire Category Theorem, Open Mapping Theorem, Closed Graph Theorem, and Banach Fixed Point Theorem. The presentation is somewhat informal, with occasional typographical errors, incomplete proofs, and missing equation references. However, the core logical flow is preserved, making it u…

People (Contributor)

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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! *

Advance Functional Analysis by Waseem Akram

admin@undisclosed.example.com (Administrator) — Mon, 25 May 2026 18:22:55 +0000

Notes of Mathematics

admin@undisclosed.example.com (Administrator) — Mon, 25 May 2026 18:19:50 +0000

Notes of Mathematics [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 resource…

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admin@undisclosed.example.com (Administrator) — Sun, 24 May 2026 17:46:31 +0000

PPSC General Information, Syllabus, Paper Pattern - [Notes]

admin@undisclosed.example.com (Administrator) — 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.

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

admin@undisclosed.example.com (Administrator) — 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$

advance-functional-analysis-waseem_akram.pdf - created

admin@undisclosed.example.com (Administrator) — Sun, 24 May 2026 17:31:51 +0000

advance-functional-analysis-waseem_akram.webp - created

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math11-pectaa-ex5-2-prof-muhammad-irfan-dogar-org.pdf - removed

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math11-pectaa-ex5-1-prof-muhammad-irfan-dogar.pdf - created

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math11-pectaa-ex5-2-prof-muhammad-irfan-dogar.pdf - created

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math11-pectaa-ex4-3-muhammad-irfan-dogar.pdf - removed

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