Erica Klarreich (Quanta Magazine)In his rapid ascent to the top of his field, James Maynard has cut a path through simple-sounding questions about prime numbers that have stumped mathematicians for centuries.
Hi, I’m Dan MacKinlay.
I’m a statistician and musician from Australia. Musician should be clear. Statistician, though, what’s that? A statistician is the exact same thing as a data scientist or machine learning researcher with the differences that there are qualifications needed to be a statistician, and that we are snarkier.
These days I work across data analysis, music, generative design and machine learning, especially for time series. I’ve been based at various times at such locations as
- Zürich, Switzerland, where I did my MSc in statistics under Professors Sara van de Geer and Didier Sornette at the Swiss Federal Institute of Technology
- Sydney, Australia, where I visualised data for the Powerhouse Museum under Seb Chan
- Bandung, Indonesia, where I worked on interactive music with Common Room and Gustaff Harriman Iskandar
Currently I am doing a PhD in statistics with Zdravko Botev at the University of New South Wales Sydney.
My current methods of interest are point process inference, compressive sensing, design grammars, sequential Monte Carlo methods, concatenative synthesis, differentiable learning, branching processes, Hilbert-space methods in high dimensional inference, stochastic differential equations and the application of all of these to economic modelling, reliability engineering and sick breakbeats.
This book provides an introduction to statistical learning methods. It is aimed for upper level undergraduate students, masters students and Ph.D. students in the non-mathematical sciences. The book also contains a number of R labs with detailed explanations on how to implement the various methods in real life settings, and should be a valuable resource for a practicing data scientist.
For a more advanced treatment of these topics: The Elements of Statistical Learning.
Slides and videos for Statistical Learning MOOC by Hastie and Tibshirani available separately here. Slides and video tutorials related to this book by Abass Al Sharif can be downloaded here.
I teach mathematics courses at University of Toronto Mississauga and Seneca College since 2016 when my family moved to Canada from Singapore. I taught full-time at Singapore Polytechnic as a math lecturer from 2012 to 2016. This is the space where I explore and share my journey of teaching mathematics, conducting education research projects, and learning about OER.
Tai-Danae Bradley (arxiv.org)This is a collection of introductory, expository notes on applied category theory, inspired by the 2018 Applied Category Theory Workshop, and in these notes we take a leisurely stroll through two themes (functorial semantics and compositionality), two constructions (monoidal categories and decorated cospans) and two examples (chemical reaction networks and natural language processing) within the field. [PDF]
Friends! I am so happy to share that my little booklet “What is Applied Category Theory?” is now available on the arXiv. It’s a collection of introductory, expository notes inspired by the ACT workshop that took place earlier this year. Enjoy! https://t.co/EPYP19z14x pic.twitter.com/O4uVhj401s
— Tai-Danae Bradley (@math3ma) September 18, 2018
See also Notes on Applied Category Theory
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A decades-old method called the “bootstrap” is enabling new discoveries about the geometry underlying all quantum theories.
In the 1960s, the charismatic physicist Geoffrey Chew espoused a radical vision of the universe, and with it, a new way of doing physics. Theorists of the era were struggling to find order in an unruly zoo of newfound particles. They wanted to know which ones were the fundamental building blocks of nature and which were composites. But Chew, a professor at the University of California, Berkeley, argued against such a distinction. “Nature is as it is because this is the only possible nature consistent with itself,” he wrote at the time. He believed he could deduce nature’s laws solely from the demand that they be self-consistent. Continue reading 👓 Physicists Uncover Geometric ‘Theory Space’ | Quanta Magazine
She won by more than Gore in 2000, Nixon in 1968 or Kennedy in 1960, it seems. And therein lies a dilemma.
Remarkable progress of quantum information theory (QIT) allowed to formulate mathematical theorems for conditions that data-transmitting or data-processing occurs with a non-negative entropy gain. However, relation of these results formulated in terms of entropy gain in quantum channels to temporal evolution of real physical systems is not thoroughly understood. Here we build on the mathematical formalism provided by QIT to formulate the quantum H-theorem in terms of physical observables. We discuss the manifestation of the second law of thermodynamics in quantum physics and uncover special situations where the second law can be violated. We further demonstrate that the typical evolution of energy-isolated quantum systems occurs with non-diminishing entropy. [1]
Weaverbot (Twitter)This is the signal for the second.
Now I’m waiting for a Shannon bot and a Weiner bot. Maybe a John McCarthy bot would be apropos too?!
This tutorial will review the basics of theory in the field of evolutionary quantitative genetics and its connections to evolution observed at various time scales. Quantitative genetics deals with the inheritance of measurements of traits that are affected by many genes. Quantitative genetic theory for natural populations was developed considerably in the period from 1970 to 1990 and up to the present, and it has been applied to a wide range of phenomena including the evolution of differences between the sexes, sexual preferences, life history traits, plasticity of traits, as well as the evolution of body size and other morphological measurements. Textbooks have not kept pace with these developments, and currently few universities offer courses in this subject aimed at evolutionary biologists. There is a need for evolutionary biologists to understand this field because of the ability to collect large amounts of data by computer, the development of statistical methods for changes of traits on evolutionary trees and for changes in a single species through time, and the realization that quantitative characters will not soon be fully explained by genomics. This tutorial aims to fill this need by reviewing basic aspects of theory and illustrating how that theory can be tested with data, both from single species and with multiple-species phylogenies. Participants will learn to use R, an open-source statistical programming language, to build and test evolutionary models. The intended participants for this tutorial are graduate students, postdocs, and junior faculty members in evolutionary biology.
César A. Hidalgo (Applied Network Science | SpringerLink)
During decades the study of networks has been divided between the efforts of social scientists and natural scientists, two groups of scholars who often do not see eye to eye. In this review I present an effort to mutually translate the work conducted by scholars from both of these academic fronts hoping to continue to unify what has become a diverging body of literature. I argue that social and natural scientists fail to see eye to eye because they have diverging academic goals. Social scientists focus on explaining how context specific social and economic mechanisms drive the structure of networks and on how networks shape social and economic outcomes. By contrast, natural scientists focus primarily on modeling network characteristics that are independent of context, since their focus is to identify universal characteristics of systems instead of context specific mechanisms. In the following pages I discuss the differences between both of these literatures by summarizing the parallel theories advanced to explain link formation and the applications used by scholars in each field to justify their approach to network science. I conclude by providing an outlook on how these literatures can be further unified.
Course Description
Complex analysis is one of the most beautiful and useful disciplines of mathematics, with applications in engineering, physics, and astronomy, as well as other branches of mathematics. This introductory course reviews the basic algebra and geometry of complex numbers; develops the theory of complex differential and integral calculus; and concludes by discussing a number of elegant theorems, including many–the fundamental theorem of algebra is one example–that are consequences of Cauchy’s integral formula. Other topics include De Moivre’s theorem, Euler’s formula, Riemann surfaces, Cauchy-Riemann equations, harmonic functions, residues, and meromorphic functions. The course should appeal to those whose work involves the application of mathematics to engineering problems as well as individuals who are interested in how complex analysis helps explain the structure and behavior of the more familiar real number system and real-variable calculus.
Prerequisites
Basic calculus or familiarity with differentiation and integration of real-valued functions.
Details
MATH X 451.37 – 268651 Introduction to Complex Analysis
Fall 2016
Time 7:00PM to 10:00PM
Dates Tuesdays, Sep 20, 2016 to Dec 06, 2016
Contact Hours 33.00
Location: UCLA, Math Sciences Building
Standard credit (3.9 units) $453.00
Instructor: Michael Miller
Register Now at UCLA
For many who will register, this certainly won’t be their first course with Dr. Miller — yes, he’s that good! But for the newcomers, I’ve written some thoughts and tips to help them more easily and quickly settle in and adjust:
Dr. Michael Miller Math Class Hints and Tips | UCLA Extension
I often recommend people to join in Mike’s classes and more often hear the refrain: “I’ve been away from math too long”, or “I don’t have the prerequisites to even begin to think about taking that course.” For people in those categories, you’re in luck! If you’ve even had a soupcon of calculus, you’ll be able to keep up here. In fact, it was a similar class exactly a decade ago by Mike Miller that got me back into mathematics. (Happy 10th math anniversary to me!)
I look forward to seeing everyone in the Fall!
Dr. Miller is back from summer vacation and emailed me this morning to say that he’s chosen the textbook for the class. We’ll be using Complex Analysis with Applications by Richard A. Silverman. [1]
(Note that there’s another introductory complex analysis textbook from Silverman that’s offered through Dover, so be sure to choose the correct one.)
As always in Dr. Miller’s classes, the text is just recommended (read: not required) and in-class notes are more than adequate. To quote him directly, “We will be using as a basic guide, but, as always, supplemented by additional material and alternate ways of looking at things.”
The bonus surprise of his email: He’s doing two quarters of Complex Analysis! So we’ll be doing both the Fall and Winter Quarters to really get some depth in the subject!
If you’re like me, you’ll probably take a look at some of the other common (and some more advanced) textbooks in the area. Since I’ve already compiled a list, I’ll share it:
