Prof. Deniz Karlı · Işık University

Lecture notes, videos and resources for my courses in probability, stochastic processes and mathematical analysis.

Lectures in Probability & Analysis · Vol. I · 2026–27Işık University · Department of Mathematics

Notes on Probability, Processes & Analysis

Deniz Karlı — Professor of Mathematics, Işık University

Abstract

This is the home of my teaching. Here you will find lecture notes, problem sets, recorded lectures and carefully chosen resources for my courses — written for students who want to understand not only how, but why.

Fig. 1. A sample path of standard Brownian motion on [0, 1], with the envelope ±2√t. Redrawn every few seconds — no two are alike.
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Courses — a table of contents.

    §2

    The Library — notes, lectures, references.

    Definition 2.1 (Lecture Notes).

    Typeset notes and problem sets for every course, organised by topic and available as PDF.

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    Definition 2.2 (Lectures on Video).

    Recorded lectures and short explainers, each paired with the notes it follows.

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    Definition 2.3 (Resources).

    Books, courses, simulations and tools I recommend, with a sentence on why each one matters.

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    “The theory of probability is at bottom nothing but common sense reduced to calculus.” — P.-S. Laplace, 1812