Jo Boaler is a professor of mathematics education at Stanford and the co-founder of youcubed.

# Archives

# THROUGH THE PROCESS | A Conversation With Applied Mathematics Professor Steven Strogatz

Join myself and Applied Mathematics Professor Steven Strogatz, author of “Infinite Powers: How Calculus Reveals the Secrets of the Universe”, as we talk about the creative powers of math, as well as poetry and the writing process, and finding the connections between the two.

If you’ve never thought of math as beautiful or creative this episode just might change your mind. I hope you will love this conversation as much as I loved being a part of it!

# Calculus Made Easy

Calculus Made Easy is a book on calculus originally published in 1910 by Silvanus P. Thompson, considered a classic and elegant introduction to the subject.

# Linear Programming | Applications Of Linear Programming

Optimization is the way of life. We all have finite resources and time and we want to make the most of them. From using your time productively to solving supply chain problems for your company – everything uses optimization. It’s an especially interesting and relevant topic in data science.

It is also a very interesting topic – it starts with simple problems, but it can get very complex. For example, sharing a bar of chocolate between siblings is a simple optimization problem. We don’t think in mathematical terms while solving it. On the other hand, devising inventory and warehousing strategy for an e-tailer can be very complex. Millions of SKUs with different popularity in different regions to be delivered in defined time and resources – you see what I mean!

Linear programming (LP) is one of the simplest ways to perform optimization. It helps you solve some very complex optimization problems by making a few simplifying assumptions. As an analyst, you are bound to come across applications and problems to be solved by Linear Programming.

For some reason, LP doesn’t get as much attention as it deserves while learning data science. So, I thought let me do justice to this awesome technique. I decided to write an article that explains Linear programming in simple English. I have kept the content as simple as possible. The idea is to get you started and excited about Linear Programming.

# Nonlinear Dynamics and Chaos – Steven Strogatz, Cornell University

This course of 25 lectures, filmed at Cornell University in Spring 2014, is intended for newcomers to nonlinear dynamics and chaos. It closely follows Prof. Strogatz’s book, “Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering.”

The mathematical treatment is friendly and informal, but still careful. Analytical methods, concrete examples, and geometric intuition are stressed. The theory is developed systematically, starting with first-order differential equations and their bifurcations, followed by phase plane analysis, limit cycles and their bifurcations, and culminating with the Lorenz equations, chaos, iterated maps, period doubling, renormalization, fractals, and strange attractors.

A unique feature of the course is its emphasis on applications. These include airplane wing vibrations, biological rhythms, insect outbreaks, chemical oscillators, chaotic waterwheels, and even a technique for using chaos to send secret messages. In each case, the scientific background is explained at an elementary level and closely integrated with the mathematical theory. The theoretical work is enlivened by frequent use of computer graphics, simulations, and videotaped demonstrations of nonlinear phenomena.

The essential prerequisite is single-variable calculus, including curve sketching, Taylor series, and separable differential equations. In a few places, multivariable calculus (partial derivatives, Jacobian matrix, divergence theorem) and linear algebra (eigenvalues and eigenvectors) are used. Fourier analysis is not assumed, and is developed where needed. Introductory physics is used throughout. Other scientific prerequisites would depend on the applications considered, but in all cases, a first course should be adequate preparation.

# Science and Sanity: An Introduction to Non-Aristotelian Systems and General Semantics

Selections from Science and Sanity represents Alfred Korzybski’s authorized abridgement of his magnum opus, Science and Sanity: An Introduction to Non-Aristotelian Systems and General Semantics. This second edition, published in response to the recent Korzybski revival, adds new introductory material and a revised index, providing an accessible introduction to Korzybski’s arguments concerning the need for a non-Aristotelian approach to knowledge, thought, perception, and language, to coincide with our non-Newtonian physics and non-Euclidean geometries, to Korzybski’s practical philosophy, applied psychology, pragmatics of human communication, and educational program. Selections from Science and Sanity serves as an excellent introduction to general semantics as a system intended to aid the individual’s adjustment to reality, enhance intellectual and creative activities, and alleviate the many social ills that have plagued humanity throughout our history.

# Principles of Systems Science (Understanding Complex Systems)

This pioneering text provides a comprehensive introduction to systems structure, function, and modeling as applied in all fields of science and engineering. Systems understanding is increasingly recognized as a key to a more holistic education and greater problem solving skills, and is also reflected in the trend toward interdisciplinary approaches to research on complex phenomena. While the concepts and components of systems science will continue to be distributed throughout the various disciplines, undergraduate degree programs in systems science are also being developed, including at the authors’ own institutions. However, the subject is approached, systems science as a basis for understanding the components and drivers of phenomena at all scales should be viewed with the same importance as a traditional liberal arts education.

*Principles* *of Systems Science* contains many graphs, illustrations, side bars, examples, and problems to enhance understanding. From basic principles of organization, complexity, abstract representations, and behavior (dynamics) to deeper aspects such as the relations between information, knowledge, computation, and system control, to higher order aspects such as auto-organization, emergence and evolution, the book provides an integrated perspective on the comprehensive nature of systems. It ends with practical aspects such as systems analysis, computer modeling, and systems engineering that demonstrate how the knowledge of systems can be used to solve problems in the real world. Each chapter is broken into parts beginning with qualitative descriptions that stand alone for students who have taken intermediate algebra. The second part presents quantitative descriptions that are based on pre-calculus and advanced algebra, providing a more formal treatment for students who have the necessary mathematical background. Numerous examples of systems from every realm of life, including the physical and biological sciences, humanities, social sciences, engineering, pre-med and pre-law, are based on the fundamental systems concepts of boundaries, components as subsystems, processes as flows of materials, energy, and messages, work accomplished, functions performed, hierarchical structures, and more. Understanding these basics enables further understanding both of how systems endure and how they may become increasingly complex and exhibit new properties or characteristics.

- Serves as a textbook for teaching systems fundamentals in any discipline or for use in an introductory course in systems science degree programs
- Addresses a wide range of audiences with different levels of mathematical sophistication
- Includes open-ended questions in special boxes intended to stimulate integrated thinking and class discussion
- Describes numerous examples of systems in science and society
- Captures the trend towards interdisciplinary research and problem solving

# Chaos: Making a New Science

*Chaos: Making a New Science* is a debut non-fiction book by James Gleick that initially introduced the principles and early development of the chaos theory to the public. It was a finalist for the National Book Award and the Pulitzer Prize in 1987, and was shortlisted for the Science Book Prize in 1989. The book was published on October 29, 1987 by Viking Books.

# Outliers: The Story of Success

In this stunning book, Malcolm Gladwell takes us on an intellectual journey through the world of “outliers”–the best and the brightest, the most famous and the most successful. He asks the question: what makes high-achievers different?

His answer is that we pay too much attention to what successful people are like, and too little attention to where they are from: that is, their culture, their family, their generation, and the idiosyncratic experiences of their upbringing. Along the way he explains the secrets of software billionaires, what it takes to be a great soccer player, why Asians are good at math, and what made the Beatles the greatest rock band.

Brilliant and entertaining, *Outliers* is a landmark work that will simultaneously delight and illuminate.