Professor Minsky laid the foundation for the field by demonstrating the possibilities of imparting common-sense reasoning to computers.
Source: Marvin Minsky, Pioneer in Artificial Intelligence, Dies at 88 – The New York Times
Professor Minsky laid the foundation for the field by demonstrating the possibilities of imparting common-sense reasoning to computers.
Source: Marvin Minsky, Pioneer in Artificial Intelligence, Dies at 88 – The New York Times
From the Physics Research Conference 2015-2016
on Thursday, November 19, 2015 at 4:00 pm
at the California Institute of Technology, East Bridge 201 – Norman Bridge Laboratory of Physics, East
All talks are intended for a broad audience, and everyone is encouraged to attend. A list of future conferences can be found here.
Sponsored by Division of Physics, Mathematics and Astronomy
Click through for the full interview: Q+A with Richard Brown, director of undergraduate studies in Johns Hopkins University’s Department of Mathematics
https://youtu.be/kg2mOl042ng
I’m sure, as always, that there are a few who are interested, but who couldn’t make the Fall lectures. Never fear, there’s a group of us that can help you get up to speed to keep pace with us during the second quarter. Just drop us a note and we’ll see what we can do.
In no field of mathematics is there such an irresistible fascination as in the theory of numbers. This course, the second in a two-quarter sequence, is an introductory, yet rigorous, survey of algebraic number theory, which evolved historically through attempts to prove Fermat’s Last Theorem. Beginning with a quick review of the previous quarter’s work, the course continues discussions on the structure of algebraic number fields, focusing particular attention on primes, units, and roots of unity in quadratic, cubic, and cyclotomic fields. Topics to be discussed include: norms and traces; the ideal class group; Minkowski’s Translate, Convex Body, and Linear Forms theorems; and Dirichlet’s Unit Theorem.
UCLA: 5137 Math Sciences
Tuesday, 7-10pm,
January 5 – March 15
11 meetings total
MATH X450.9
3.00 units
We’ll be using Introductory Algebraic Number Theory by Saban Alaca and Kenneth S. Williams (Cambridge University Press, 2003, ISBN: 978-0521183048).
You can also read more about her appearance from Category Theorist John Carlos Baez here: Cakes, Custard, Categories and Colbert | The n-Category Café
My brief review of her book on GoodReads.com:
How to Bake Pi: An Edible Exploration of the Mathematics of Mathematics by Eugenia Cheng
My rating: 4 of 5 starsWhile most of the book is material I’ve known for a long time, it’s very well structured and presented in a clean and clear manner. Though a small portion is about category theory and gives some of the “flavor” of the subject, the majority is about how abstract mathematics works in general.
I’d recommend this to anyone who wants to have a clear picture of what mathematics really is or how it should be properly thought about and practiced (hint: it’s not the pablum you memorized in high school or even in calculus or linear algebra). Many books talk about the beauty of math, while this one actually makes steps towards actually showing the reader how to appreciate that beauty.
Like many popular books about math, this one actually has very little that goes beyond the 5th grade level, but in examples that are very helpfully illuminating given their elementary nature. The extended food metaphors and recipes throughout the book fit in wonderfully with the abstract nature of math – perhaps this is why I love cooking so much myself.
I wish I’d read this book in high school to have a better picture of the forest of mathematics.
More thoughts to come…
Instagram filter used: Normal
Photo taken at: UCLA Math Sciences Building
The Winter Q-BIO Quantitative Biology Meeting is coming up at the Sheraton Waikiki in Oahu, HI, USA
A predictive understanding of living systems is a prerequisite for designed manipulation in bioengineering and informed intervention in medicine. Such an understanding requires quantitative measurements, mathematical analysis, and theoretical abstraction. The advent of powerful measurement technologies and computing capacity has positioned biology to drive the next scientific revolution. A defining goal of Quantitative Biology (qBIO) is the development of general principles that arise from networks of interacting elements that initially defy conceptual reasoning. The use of model organisms for the discovery of general principles has a rich tradition in biology, and at a fundamental level the philosophy of qBIO resonates with most molecular and cell biologists. New challenges arise from the complexity inherent in networks, which require mathematical modeling and computational simulation to develop conceptual “guideposts” that can be used to generate testable hypotheses, guide analyses, and organize “big data.”
The Winter q-bio meeting welcomes scientists and engineers who are interested in all areas of q-bio. For 2016, the meeting will be hosted at the Sheraton Waikiki, which is located in Honolulu, on the island of Oahu. The resort is known for its breathtaking oceanfront views, a first-of-its-kind recently opened “Superpool” and many award-winning dining venues. Registration and accommodation information can be found via the links at the top of the page.
A Japanese mathematician claims to have solved one of the most important problems in his field. The trouble is, hardly anyone can work out whether he's right.
The biggest mystery in mathematics
This article in Nature is just wonderful. Everyone will find it interesting, but those in the Algebraic Number Theory class this fall will be particularly interested in the topic – by the way, it’s not too late to join the class. After spending some time over the summer looking at Category Theory, I’m tempted to tackle Mochizuki’s proof as I’m intrigued at new methods in mathematical thinking (and explaining.)
The abc conjecture refers to numerical expressions of the type a + b = c. The statement, which comes in several slightly different versions, concerns the prime numbers that divide each of the quantities a, b and c. Every whole number, or integer, can be expressed in an essentially unique way as a product of prime numbers — those that cannot be further factored out into smaller whole numbers: for example, 15 = 3 × 5 or 84 = 2 × 2 × 3 × 7. In principle, the prime factors of a and b have no connection to those of their sum, c. But the abc conjecture links them together. It presumes, roughly, that if a lot of small primes divide a and b then only a few, large ones divide c.
Thanks to Rama for bringing this to my attention!
Invariably the handful of new students every year eventually figure the logistics of campus out, but it’s easier and more fun to know some of the options available before you’re comfortable halfway through the class. To help get you over the initial hump, I’ll share a few of the common questions and tips to help get you oriented. Others are welcome to add comments and suggestions below. If you have any questions, feel free to ask anyone in the class, we’re all happy to help.
First things first, for those who’ve never visited UCLA before, here’s a map of campus to help you orient yourself. Using the Waze app on your smartphone can also be incredibly helpful in getting to campus more quickly through the tail end of rush hour traffic.
Whether you’re a professional mathematician, engineer, physicist, physician, or even a hobbyist interested in mathematics you’ll be sure to get something interesting out of Dr. Miller’s math courses, not to mention the camaraderie of 20-30 other “regulars” with widely varying backgrounds (from actors to surgeons and evolutionary theorists to engineers) who’ve been taking almost everything Mike has offered over the years (and yes, he’s THAT good — we’re sure you’ll be addicted too.) Whether you’ve been away from serious math for decades or use it every day or even if you’ve never gone past Calculus or Linear Algebra, this is bound to be the most entertaining thing you can do with your Tuesday nights in the Autumn and Winter. If you’re not sure what you’re getting into (or are scared a bit by the course description), I highly encourage to come and join us for at least the first class before you pass up on the opportunity. I’ll mention that the greater majority of new students to Mike’s classes join the ever-growing group of regulars who take almost everything he teaches subsequently.
Don’t be intimidated if you feel like everyone in the class knows each other fairly well — most of us do. Dr. Miller and mathematics can be addictive so many of us have been taking classes from him for 5-20+ years, and over time we’ve come to know each other.
If you’ve never been to one of Dr. Miller’s classes before, they’re fairly informal and he’s very open to questions from those who don’t understand any of the concepts or follow his reasoning. He’s a retired mathematician from RAND and long-time math professor at UCLA. Students run the gamut from the very serious who read multiple textbooks and do every homework problem to hobbyists who enjoy listening to the lectures and don’t take the class for a grade of any sort (and nearly every stripe in between). He’ll often recommend a textbook that he intends to follow, but it’s never been a “requirement” and more often that not, the bookstore doesn’t list or carry his textbook until the week before class. (Class insiders will usually find out about the book months before class and post it to the Google Group – see below).
His class notes are more than sufficient for making it through the class and doing the assigned (optional) homework. He typically hands out homework in handout form, so the textbook is rarely, if ever, required to make it through the class. Many students will often be seen reading various other texts relating to the topic at hand as they desire. Usually he’ll spend an 45-60 minutes at the opening of each class after the first to go over homework problems or questions that anyone has.
For those taking the class for a grade or pass/fail, his usual policy is to assign a take home problem set around week 9 or 10 to be handed in at the penultimate class. [As a caveat, make sure you check his current policy on grading as things may change, but the preceding has been the usual policy for a decade or more.]
Lot 9 – Located at the northern terminus of Westwood Boulevard, one can purchase a parking pass for about $12 a day at the kiosk in the middle of the street just before Westwood Blvd. ends. The kiosk is also conveniently located right next to the parking structure. If there’s a basketball game or some other major event, Lot 8 is just across the street as well, though it’s just a tad further away from the Math Sciences Building. Since more of the class uses this as their parking structure of choice, there is always a fairly large group walking back there after class for the more security conscious.
Lot 2 – Located off of Hilgard Avenue, this is another common option for easy parking as well. While fairly close to class, not as many use it as it’s on the quieter/darker side of campus and can be a bit more of a security issue for the reticent.
Tip: For those opting for on-campus parking, one can usually purchase a quarter-long parking pass for a small discount at the beginning of the term.
Westwood Village and Neighborhood – Those looking for less expensive options street parking is available in the surrounding community, but use care to check signs and parking meters as you assuredly will get a ticket. Most meters in the surrounding neighborhoods end at either 6pm or 8pm making parking virtually free (assuming you’re willing to circle the neighborhood to find one of the few open spots.)
There are a huge variety of lots available in the Village for a range of prices, but the two most common, inexpensive, and closer options seem to be:
More often than not a group of between 4 and 15 students will get together every evening before class for a quick bit to eat and to catch up and chat. This has always been an informal group and anyone from class is more than welcome to join. Typically we’ll all meet in the main dining hall of Ackerman Union (Terrace Foodcourt, Ackerman Level 1) between 6 and 6:30 (some with longer commutes will arrive as early as 3-4pm, but this can vary) and dine until about 6:55pm at which time we walk over to class.
The food options on Ackerman Level 1 include Panda Express, Rubio’s Tacos, Sbarro, Wolfgang Puck, and Greenhouse along with some snack options including Wetzel’s Pretzels and a candy store. One level down on Ackerman A-level is a Taco Bell, Carl’s Jr., Jamba Juice, Kikka, Buzz, and Curbside, though one could get takeout and meet the rest of the “gang” upstairs.
There are also a number of other on-campus options as well though many are a reasonable hike from the class location. The second-closest to class is the Court of Sciences Student Center with a Subway, Yoshinoya, Bombshelter Bistro, and Fusion.
Naturally, for those walking up from Westwood Village, there are additional fast food options like In-N-Out, Chick-fil-A, Subway, and many others.
For those who’ve already eaten or aren’t hungry, you’ll often find one or more of us browsing the math and science sections of the campus bookstore on the ground level of Ackerman Union to kill time before class. Otherwise there are usually a handful of us who arrive a half an hour early and camp out in the classroom itself (though this can often be dauntingly quiet as most use the chance to catch up on reading here.) If you arrive really early, there are a number of libraries and study places on campus. Boelter Hall has a nice math/science library on the 8th Floor.
Usually about halfway through class we’ll take a 10-12 minute coffee break. For those with a caffeine habit or snacking urges, there are a few options:
Kerckhoff Hall Coffee Shop is just a building or two over and is open late as snack stop and study location. They offer coffee and various beverages as well as snacks, bagels, pastries, and ice cream. Usually 5-10 people will wander over as a group to pick up something quick.
The Math Sciences Breezeway, just outside of class, has a variety of soda, coffee, and vending machines with a range of beverages and snacks. Just a short walk around the corner will reveal another bank of vending machines if your vice isn’t covered. The majority of class will congregate in the breezeway to chat informally during the break.
The Court of Sciences Student Center, a four minute walk South, with the restaurant options noted above if you need something quick and more substantial, though few students use this option at the break.
Bathrooms – The closest bathrooms to class are typically on the 5th floor of the Math Sciences Building. The women’s is just inside the breezeway doors and slightly to the left. The men’s rooms are a bit further and are either upstairs on the 6th floor (above the women’s), or a hike down the hall to the left and into Boelter hall. I’m sure the adventurous may find others, but take care not to get lost.
Over the years, as an informal resource, members of the class have created and joined a private Google Group (essentially an email list-serv) to share thoughts, ideas, events, and ask questions of each other. There are over 50 people in the group, most of whom are past Miller students, though there are a few other various mathematicians, physicists, engineers, and even professors. You can request to join the private group to see the resources available there. We only ask that you keep things professional and civil and remember that replying to all reaches a fairly large group of friends. Browsing through past messages will give you an idea of the types of posts you can expect. The interface allows you to set your receipt preferences to one email per message posted, daily digest, weekly digest, or no email (you’re responsible for checking the web yourself), so be sure you have the setting you require as some messages are more timely than others. There are usually only 1-2 posts per week, so don’t expect to be inundated.
Depending on students’ moods, time requirements, and interests, we’ve arranged informal study groups for class through the Google Group above. Additionally, since Dr. Miller only teaches during the Fall and Winter quarters, some of us also take the opportunity to set up informal courses during the Spring/Summer depending on interests. In the past, we’ve informally studied Lie Groups, Quantum Mechanics, Algebraic Geometry, and Category Theory in smaller groups on the side.
As a class resource, some of us share a document repository via Dropbox. If you’d like access, please make a post to the Google Group.
Many people within the class use Livescribe.com digital pens to capture not only the written notes but the audio discussion that occurred in class as well (the technology also links the two together to make it easier to jump around within a particular lecture). If it helps to have a copy of these notes, please let one of the users know you’d like them – we’re usually pretty happy to share. If you miss a class (sick, traveling, etc.) please let one of us know as the notes are so unique that it will be almost like you didn’t miss anything at all.
You can typically receive a link to the downloadable version of the notes in Livescribe’s Pencast .pdf format. This is a special .pdf file but it’s a bit larger in size because it has an embedded audio file in it that is playable with the more recent version of Adobe Reader X (or above) installed. (This means to get the most out of the file you have to download the file and open it in Reader X to get the audio portion. You can view the written portion in most clients, you’ll just be missing out on all the real fun and value of the full file.) With the notes, you should be able to toggle the settings in the file to read and listen to the notes almost as if you were attending the class live.
Viewing and Playing a Pencast PDF
Pencast PDF is a new format of notes and audio that can play in Adobe Reader X or above.
You can open a Pencast PDF as you would other PDF files in Adobe Reader X. The main difference is that a Pencast PDF can contain ink that has associated audio—called “active ink”. Click active ink to play its audio. This is just like playing a Pencast from Livescribe Online or in Livescribe Desktop. When you first view a notebook page, active ink appears in green type. When you click active ink, it turns gray and the audio starts playing. As audio playback continues, the gray ink turns green in synchronization with the audio. Non-active ink (ink without audio) is black and does not change appearance.Audio Control Bar
Pencast PDFs have an audio control bar for playing, pausing, and stopping audio playback. The control bar also has jump controls, bookmarks (stars), and an audio timeline control.
Active Ink View Button
There is also an active ink view button. Click this button to toggle the “unwritten” color of active ink from gray to invisible. In the default (gray) setting, the gray words turn green as the audio plays. In the invisible setting, green words seem to write themselves on blank paper as the audio plays.
For those interested in past years’ topics, here’s the list I’ve been able to put together thus far:
Fall 2006: Complex Analysis
Winter 2007: Field Theory
Fall 2007: Algebraic Topology
Winter 2008: Integer Partitions
Fall 2008: Calculus on Manifolds
Winter 2009: Calculus on Manifolds: The Sequel
Fall 2009: Group Theory
Winter 2010: Galois Theory
Fall 2010: Differential Geometry
Winter 2011: Differential Geometry II
Fall 2011: p-Adic Analysis
Winter 2012: Group Representations
Fall 2012: Set Theory
Winter 2013: Functional Analysis
Fall 2013: Number Theory (Skipped)
Winter 2014: Measure Theory
Fall 2014: Introduction to Lie Groups and Lie Algebras Part I
Winter 2015: Introduction to Lie Groups and Lie Algebras Part II
Fall 2015: Algebraic Number Theory
Winter 2016: Algebraic Number Theory: The Sequel
Fall 2016: Introduction to Complex Analysis, Part I
Winter 2017: Introduction to Complex Analysis, Part II
Fall 2017: Introduction to Algebraic Geometry
Winter 2018: Introduction to Algebraic Geometry: The Sequel
Fall 2018: Gems and Astonishments of Mathematics Past and Present
Winter 2019: Introduction to Category Theory
Fall 2019: ??
Winter 2020: ??
Fall 2020: Cancelled due to coronavirus pandemic
Winter 2021: Cancelled due to coronavirus pandemic
Fall 2021: Differential Topology
Winter 2022: Differential Topology (not offered due to remote-only option for public health/COVID-19 reasons)
Fall 2022: Theory and Applications of Continued Fractions
Winter 2023: Nothing offered due to Extension scheduling issues
Fall 2023: Topics in Ring Theory and Modules
“The Mathematics Literature Project intends to survey the state of the freely accessible mathematics literature. In particular, it will index freely accessible URLs for mathematics articles. These are legitimately hosted copies of the article (i.e. at publishers, the arXiv, institutional repositories, or authors’ homepages), which are freely available in any browser, anywhere in the world.”
Physicist Stephen Hawking made a splash this week when he announced that he had solved a vexing conundrum that had puzzled generations of leading physicists -- including the 73-year-old scientific superstar himself -- for the better part of a half-century.
Like a kid anxiously awaiting Christmas morning, I spent some time refreshing UCLA Extension’s web page over the weekend in hopes of seeing the announcement of Mike Miller’s Fall math course with no results.
I checked again a half hour ago and their site was down!
Refreshing, refreshing, refreshing… and now it’s live again with:
Mike Miller is teaching Algebraic Number Theory in the Fall!
Register quickly before it fills up. And let the pool for the guesses about which textbook he’ll recommend begin!
Algebraic Number Theory
MATH X 450.8 | 3.00 units
In no field of mathematics is there such an irresistible fascination as in the theory of numbers. This course, the first in a two-quarter sequence, is an introductory, yet rigorous, survey of algebraic number theory, which evolved historically through attempts to prove Fermat’s Last Theorem. Beginning with a quick review of primality and unique factorization for ordinary integers, the course extends these notions to more exotic domains: quadratic, cubic, cyclotomic, and general number fields. This development is then applied to the representation of integers as sums of squares and, more generally, to classic Diophantine equations. Topics to be discussed include: Euclidean, principal ideal, and Noetherian domains; integral bases; binary quadratic forms; algebraic field extensions; and several remarkable theorems/conjectures of Ramanujan.
UCLA: 5137 Math Sciences
Tuesday, 7-10pm,
September 22 – December 8
11 meetings total
(no mtg 11/17)
See you all in just a few weeks!
As many may know or have already heard, Dr. Mike Miller, a retired mathematician from RAND and long-time math professor at UCLA, has been offering incredibly inexpensive upper level undergraduate and graduate level math courses for 30+ years through UCLA Extension.
Whether you’re a professional mathematician, engineer, physicist, physician, or simply a hobbyist interested in mathematics you’ll be sure to get something interesting out of this course, not to mention the camaraderie of 20-30 other “regulars” with widely varying backgrounds (actors to surgeons and evolutionary theorists to engineers) who’ve been taking almost everything Mike has offered over the years. Once most new students have taken one class, they’re incredibly prone to want to take them all (and yes, he’s THAT good — we’re sure you’ll be addicted too.)
Even if it’s been years since you last took calculus or linear algebra, Mike (and usually the rest of the class) will help you get quickly back up to speed to delve into what is often a very deep subject. Though there are a handful who will want to learn the subject for specific applications, naturally, it’s simply a beautiful and elegant subject for those who just want to meander their way through higher mathematics for the fun of it (this will probably comprise the largest majority of the class by the way.)
Whether you’ve been away from serious math for decades or use it every day or even if you’ve never gone past calculus, this is bound to be the most entertaining thing you can do with your Tuesday nights in the fall. If you’re not sure what you’re getting into (or are scared a bit by the course description), I highly encourage to come and join us for at least the first class before you pass up on the opportunity – there’s no need to preregister or prepay if you’re unsure. I’ll mention that the greater majority of new students to Mike’s classes join the ever-growing group of regulars who take almost everything he teaches subsequently.
For the reticent, I’ll mention that one of the first courses I took from Mike was Algebraic Topology which generally requires a few semesters of Abstract Algebra and a semester of Topology as prerequisites. I’d taken neither of these prerequisites, but due to Mike’s excellent lecture style and desire to make everything comprehensible to the broadest number of students, I was able to do exceedingly well in the course. Also keep in mind that you can register to take the class for a grade, pass/fail, or even no grade at all to suit your needs/lifestyle.
Update (8/19/15) Per my email conversation with Dr. Miller, despite that neither the Extension website nor the bookstore have a book listed for the class yet, he’s going to be recommending Introductory Algebraic Number Theory by Saban Alaca and Kenneth S. Williams (Cambridge University Press, 2003, ISBN: 978-0521183048).
How a mathematical breakthrough from the 1960s now powers everything from spacecraft to cell phones.