LECTURES, ESSAYS, AND PODCASTS



Ten Simple Rules for Mathematical Writing


THE SLIDE PRESENTATION

Mathematical writing is the type of writing where mathematics is used as a primary means for expression, deduction, or problem solving. It is fundamentally different from creative and expository writing for two main reasons:

As a result, many of the rules and suggestions found in writing style manuals are inadequate and/or do not apply. We propose an approach to mathematical writing, based on a set of simple composition rules. These rules are outlined in a slide presentation from an April 2002 lecture at MIT (edited later), and focus on the structure of the entire document (the content and the interconnections of different parts):

* Organize in segments

* Write segments linearly

* Consider a hierarchical development

* Use consistent notation and nomenclature

* State results consistently

* Don't underexplain - don't overexplain

* Tell them what you'll tell them

* Use suggestive references

* Consider examples and counterexamples

* Use visualization when possible

The lecture slides can be freely downloaded and used for personal or educational purposes.


Ten Simple Rules Slides
A PODCAST BASED ON THE SLIDE PRESENTATION

Ten Simple Rules Podcast

It can be used while viewing the slides


A CHATGPT-GENERATED ESSAY BASED ON THE SLIDE PRESENTATION AND THE TRANSCRIPT OF THE PODCAST

Ten Simple Rules Essay by ChatGPT



Podcasts for Some of my Books and Other Writings

These are podcasts generated by Google NotebooksLM. Click on the podcast, and when the screen opens, click on the right to hear the audio podcast description. Type at the bottom questions about the book content!

A Course in Reinforcement Learning. A 18 mins audio description of the 500-page, ASU course textbook by D. Bertsekas (2025, 2nd edition).

Lessons from AlphaZero for Optimal, Model Predictive, and Adaptive Control. A 14 mins audio description of the monograph by D. Bertsekas, 2022. The book is focused on the synergy between the off-line training and on-line play algorithms, based on the algorithmic framework of Newton's method.

Rollout, Policy Iteration, and Reinforcement Learning. A 14 mins audio description of the monograph by D. Bertsekas, 2020. The book is focused on approximate policy iteration, rollout (which is a single policy iteration), and distributed implementations of these algorithms, particularly for multiagent systems.

Model Predictive Control, Reinforcement Learning, and Newton's Method. A 20-minute audio supplement to the preceding two podcasts. It outlines a unifying framework that links model predictive control (MPC), value-space approximation in reinforcement learning (RL), and dynamic programming. It highlights the two algorithms common to these approaches - off-line training and on-line play - and explains how their synergy is grounded in the use of Newton's method for solving the Bellman equation. This perspective clarifies the broad applicability and effectiveness of both MPC and RL/value-space approximation methods.

Convex Optimization Theory. A 19 mins audio description of the textbook by D. Bertsekas, 2009. The book is focused on the mathematical theory of convexity, the theory of convex function, convex optimization and duality, and the min-common/max-crossing geometric duality framework that underlies duality theory.

Min-Common/Max-Crossing Duality. A focused 19 mins audio supplement to the Convex Optimization Theory book above. It develops its underlying geometric, highly visual duality framework. This framework is also described in the video A 60-Year Journey in Convex Optimization, a lecture on the history and the evolution of the subject.

Convex Optimization Algorithms. A 22-minute audio overview of D. Bertsekas's 2009 textbook on the algorithmic theory of convex optimization. The book presents key optimization models, including Lagrange and Fenchel duality, and covers major algorithmic frameworks such as subgradient, cutting-plane, proximal, and interior-point methods. It also examines iterative descent techniques - gradient projection, Newton, and coordinate descent - along with their incremental and distributed asynchronous variants.

Network Optimization: Continuous and Discrete Models. A 19 mins audio description of the network optimization book by D. Bertsekas, 1998. The book is focused on duality theory and algorithms for a broad variety of network optimization problems. There is a special emphasis on the author's original work on auction algorithms.

Auction Algorithms for Assignment and Network Optimization. A 20 mins audio description of the auction algorithm and its extensions, which supplements the preceding book. It starts with the original 1979 paper and extends to the more recent 2023 work on new types of auction algorithms: aggressive auction, conservative auction, cooperative auction, and mixtures of these. The podcast is focused on the assignment problem, but provides an entry point to algorithms for a broader variety of network optimization problems.

Nonlinear Programming. A 19 mins audio description of the 840-pages textbook by D. Bertsekas, 1916. This extensive text provides a comprehensive overview of nonlinear optimization problems, ranging from unconstrained to constrained problems. It explores various algorithmic approaches, including gradient methods, Newton's method, conjugate direction methods, and quasi-Newton methods, analyzing their convergence properties and rates. The discussion also encompasses duality theory, augmented Lagrangian methods, ADMM, and penalty methods, detailing their application in solving complex optimization challenges like network flow and discrete optimization problems. Emphasis is placed on both the theoretical underpinnings and practical considerations for implementing these optimization techniques.

Parallel and Distributed Computation: Numerical Methods. A 33 mins audio description of the 700-page monograph by D. Bertsekas and J. Tsitsiklis, 1989. The book has received multiple awards, and is the chronologically first book with a focus on distributed asynchronous numerical computation, among others.

Neuro-Dynamic Programming. A 25 mins audio description of the 500-page monograph by D. Bertsekas and J. Tsitsiklis, 1996. The book has received multiple awards, and is the chronologically first book in reinforcement learning.

Dynamic Programming and Optimal Control, Vol. I. A 20 mins audio description of the first of two volumes of the comprehensive textbook on dynamic programming by D. Bertsekas, 2017. The first volume is oriented towards modeling, conceptualization, and finite-horizon problems, but also includes a substantive introduction to infinite horizon problems that is suitable for classroom use. The text contains many illustrations, worked-out examples, and exercises.

Dynamic Programming and Optimal Control, Vol. II. A 12 mins audio description of the first of two volumes of the comprehensive textbook on dynamic programming by D. Bertsekas, 2018. The second volume is oriented towards mathematical analysis and computation, treats infinite horizon problems extensively, and provides an up-to-date account of approximate large-scale dynamic programming and reinforcement learning. The text contains many illustrations, worked-out examples, and exercises.

Abstract Dynamic Programming. A 20-minute audio overview of the 3rd edition of D. Bertsekas' 2022 mathematical monograph on the theory and algorithms of optimal control. The book examines both the theoretical foundations and a range of algorithmic approaches, covering contractive models - where the dynamic programming mapping is a contraction - and noncontractive models, which involve more challenging cases such as shortest path problems and linear–quadratic optimal control. It discusses value iteration (VI) and policy iteration (PI) in their exact, approximate, and asynchronous forms, as well as optimistic PI and Lambda--policy iteration. The text also extends the abstract DP framework to minimax control and zero-sum games.

Academia, Art, and Life. A 20-minute audio overview of an essay that explores the nature of artistry within academic life. At its core, the essay seeks to expand the definition of an artist beyond traditional creative fields, suggesting that artistry is defined not by domain, but by how and why one works. This perspective gives rise to a three-tiered framework of roles - technician, craftsman, and artist - distinguished by the degree of autonomy in setting goals and designing processes to achieve the goals. Within this framework, the essay examines related themes such as talent, mastery, inspiration, creativity, and artistic integrity, especially as they arise in teaching, research, and the broader landscape of academic life. The essay makes no claims to scholarship - its aim is simply to share reflections from my journey through art and academia.