The Department of Mathematics at Berkeley is generally recognized as one of the broadest, liveliest, and most distinguished departments of mathematics in the world. With approximately 55 regular faculty members representing most of the major fields of current research, along with 25 to 30 post-doctoral scholars, graduate students, over undergraduate majors, one of the finest mathematics libraries in the nation, and situated in a favorable climate in one of America's most exciting and cosmopolitan centers for mathematics research and teaching, Berkeley has become a favorite location for the study of mathematics by students and faculty from all over the world.

Sincewhen the quality of its mathematics faculty was ranked eleventh in the nation by the American Council of Education, Berkeley improved dramatically, reaching fourth place inand second place in It achieved an unsurpassed ranking inwhich was reaffirmed in the most recent survey. The Department offices are located on the top four floors of Evans Hall, situated in the northeast quadrant of Berkeley's scenic hillside campus.

Within this building, the Department has excellent facilities for a flourishing mathematical community. These include an square foot Common Room on the tenth floor overlooking San Francisco Bay, an outstanding computer laboratory on the seventh floor, 26 classrooms especially designed for mathematics instruction on the ground floor, and a calculus computer lab on the basement floor.

The Mathematics Library on the first floor of Evans Hall, part of the system of University of California Librariesprovides researchers and students with access to world-class collections.

Berkeley is increasingly interested in developing the talents of outstanding mathematics students and has a number of challenging honors-level courses. The Department encourages all major students to participate in the annual William Lowell Putnam Mathematical Competition. Additionally, the Department sponsors undergraduate teams in the annual Mathematical Contest in Modeling in which teams of 3 people write mathematical solutions apply splines to landscape real-life problems.

An active Mathematics Undergraduate Student Association MUSAof which all departmental majors are automatically members, contributes to making Berkeley a stimulating and rewarding place to study mathematics. Moreover, Womxn in Mathematics at Berkeley WIM serves to foster a community and provide a network amongst the undergraduate women in mathematics at Cal. Berkeley's mathematics education program is greatly enriched by its large number of graduate students, postdoctoral faculty and fellows, and visiting teaching in residence each year.

They come from all over the world to teach courses, participate in seminars, collaborate in research, give talks at the weekly Mathematics Colloquium, and be available as consultants. An affiliated interdisciplinary group, with its own doctoral program, is the Group in Logic and the Methodology of Science. These groups run seminars, workshops and other activities and support graduate student and postdoctoral fellows in their areas of interest. The Department has several graduate student groups : the Mathematics Graduate Student Association MGSAcomprising all graduate students, the Noetherian Ringa group of women in mathematics, Unbounded Representation Ureppromoting dialogue on diversity in the math community, and a student lecture series, Many Cheerful Facts.

In a beautifully designed building on the hills above the Berkeley campus overlooking San Francisco Bay, about 1, mathematicians from around the world come each year to participate in research programs in a wide variety of mathematical topics.

The combined and cooperative efforts of the Department, the Center, and the Institute provide a program of mathematics courses, workshops, seminars, and colloquia of remarkable variety and exciting intensity. The Department of Mathematicsfaculty, staff, and studentsis committed to fostering an atmosphere of respect, collegiality, and sensitivity. The math department upholds the policies of the university regarding discrimination and harassment. But beyond that, we strive to provide a welcoming and supportive environment for all, regardless of other characteristics that are irrelevant to the pursuit of mathematics, for example, size or socioeconomic status, in addition to the protected categories outlined in UC policy.

In most situations, simple common sense and good judgment should suffice as guidance, but we appreciate that some questions of appropriate behavior can be more complex and subtle. Instead of focusing on this fine line, we encourage faculty, staff, and students to strive for their actions in all contexts to be genuinely respectful and supportive rather than merely appropriate. For guidance about your own behavior, or if you think you have experienced or witnessed discrimination or harassment of any kind, we urge you to seek advice and support.

Any member of the faculty or staff whom you trust is an appropriate contact person, in particular the Chair and Vice Chairsor the university resources listed below. When bringing concerns forward about discrimination or harassment, we will strive to treat these with discretion, respecting the privacy of individuals insofar as possible, but in some cases policy or law may require that department members contact an appropriate university authority.

Here is the list of university resources. In particular, the ombuds offices offer confidential advice and assistance with dispute resolution, and counseling centers in University Health Services Services offer confidential counseling and support:.

Office for the Prevention of Harassment and Discrimination. Ombuds Office for Student and Postdoctoral Appointees. Faculty Ombudsperson.

Jump to Navigation. About the Department.Libraries and resellers, please contact cust-serv ams. See our librarian page for additional eBook ordering options.

Edited by Zvezdelina Stankova; Tom Rike. Many mathematicians have been drawn to mathematics through their experience with math circles : extracurricular programs exposing teenage students to advanced mathematical topics and a myriad of problem solving techniques and inspiring in them a lifelong love for mathematics.

Over the last decade, 50 instructorsâ€”from university professors to high school teachers to business tycoonsâ€”have shared their passion for mathematics by delivering more than BMC sessions full of mathematical challenges and wonders.

Based on a dozen of these sessions, this book encompasses a wide variety of enticing mathematical topics: from inversion in the plane to circle geometry; from combinatorics to Rubik's cube and abstract algebra; from number theory to mass point theory; from complex numbers to game theory via invariants and monovariants.

The treatments of these subjects encompass every significant method of proof and emphasize ways of thinking and reasoning via problem solving techniques. Also featured are problems, ranging from beginner to intermediate level, with occasional peaks of advanced problems and even some open questions. The book encourages you to apply the newly acquired knowledge to problems and guides you along the way, but rarely gives you ready answers.

The mathematical world is huge: you'll never know everything, but you'll learn where to find things, how to connect and use them. The rewards will be substantial. In the interest of fostering a greater awareness and appreciation of mathematics and its connections to other disciplines and everyday life, MSRI and the AMS are publishing books in the Mathematical Circles Library series as a service to young people, their parents and teachers, and the mathematics profession.

High school teachers and students interested in mathematical problem solving; college professors and research mathematicians interested in the mathematical education of talented middle and high school students.

It is written with enthusiasm and flair; the book breathes love for mathematics and the desire to convey and share it with the reader.

The editors deserve praise for producing a coherent style that is followed throughout. On the whole, the book is thoughtfully organized and well written. Know that ebook versions of most of our titles are still available and may be downloaded immediately after purchase.

AMS Homepage. Join our email list. Sign up. Ordering on the AMS Bookstore is limited to individuals for personal use only. Advanced search. Abstract: Many mathematicians have been drawn to mathematics through their experience with math circles : extracurricular programs exposing teenage students to advanced mathematical topics and a myriad of problem solving techniques and inspiring in them a lifelong love for mathematics.

Volume: 1. Publication Month and Year: Copyright Year: Page Count: Cover Type: Softcover. Print ISBN Online ISBN Print ISSN: Online ISSN: Primary MSC: Applied Math? MAA Book? Electronic Media? Apparel or Gift: false.Math Circles bring mathematicians and mathematical scientists into direct contact with pre-college students.

These students and sometimes their teachers meet with mathematics professionals in an informal setting, after school or on weekends, to work on interesting problems or topics in mathematics. These interactions get students excited about mathematics and provide them with a community to foster their passion for mathematical thinking. The Berkeley Math Circle BMC is intended for talented middle- and high-school students who are interested in extending their mathematical knowledge and skills well beyond what their curriculum offers.

The majority of the sessions are split into two separate groups: for advanced and for beginning students. The Marin Math Circle brings together students who are interested in exploring new mathematical topics and challenging problems. This is an extraordinary activity for students who enjoy mathematics and want to learn more. The San Francisco Math Circle SFMC is intended primarily for middle school students in San Francisco who are interested in extending their mathematical knowledge and skills well beyond what their curriculum offers.

It's intended for middle and high school students, although anyone is welcome. The emphasis is to show teachers some beautiful and entertaining mathematics as opposed to telling them what or how they should teach.

For K Educators. Critical Issues. Math Circles. Julia Robinson Mathematics Festival. Professional Development. Illustrative Math Webinars. What is a Math Circle?At first, a room is empty.

Each minute, either one person enters or two people leave. After exactly minutes, could the room contain people? Show that if every room in a house has an even number of doors, then the number of outside entrance doors must be even as well.

Lockers in a row are numbered. At first, all the lockers are closed. A person walks by, and opens every other locker, starting with locker 2.

Thus lockers are open. Then another person changes the state of every 4th locker, starting with 4, etc. This process continues until no more lockers can be altered. Which lockers will be closed? Let represent an arbitrary arrangement of the numbers. Prove that, if is odd, the product.

**The Berkeley Math Circle**

A bubble-chamber contains three types of sub-atomic particles: 10 particles of type X, 11 of type Y, of type Z. Whenever an X- and Y-particle collide, they both become Z-particles. Likewise, Y- and Z- particles collide and become X-particles and X- and Z-particles become Y-particles upon collision. Can the particles in the bubble chamber evolve so that only one type is present?

Let be distinct points in the plane. Connect the points with the line segments. Can one draw a line which passes through the interior of every one of these segments? Is is possible to tile a rectangle with rectangles? Start with a set of lattice points.Residential students and participating commuting students will eat breakfast in the campus dining hall.

Students will be supervised by their RAs. Commuting students should be dropped off at the designated area anytime between AM and AM. There will be a TA to greet them and accompany them to the classroom. For the first 50 minutes of the course, students will receive instruction from an expert in either number theory or combinatorics. Lessons will incorporate interactive activities and lectures that are both informative and engaging.

They will also be tasked with communicating their findings to their peers and the instructor. Students will attend their chosen elective course. Each course varies by topic and instructor, but all have an academic focus. Students will eat lunch at the campus dining hall and will be supervised by TAs and the site coordinator.

Food in the dining halls is served buffet-style, offering a variety of options. The format of the second primary course will be the same as for the first. A minute lesson will be followed by a minute problem session. After an intense day of mathematics, students have the chance to relax and unwind by playing board games and eating snacks with their peers. Afternoon activities include professor talks, lectures in special topics, and preparation for the capstone project.

Special topics include lessons on cryptography leading up to the Cryptography Scavenger Hunt, expected value and probability to prepare for the Math Circle Casino, and more. The capstone project, presented on the last day of the program, is a poster in which students communicate their understanding of a topic of their choice. Residential students and participating commuting students will eat dinner in the campus dining hall.

Commuting students should be picked up at the designated pick-up area at PM. There will be a TA to make sure that everyone is picked up. Evening activities are organized by the RAs and range from movie nights to ultimate frisbee. Activities are designed to build a sense of trust and community among the students. At PM, students must be in their bed with the lights out. Commuting Students. Residential Students.

Lunch AM - PM. Pick-Up Commuting PM.Learn about the people and activities that make UC Berkeley one of the best places in the world for advanced research, graduate and undergraduate study in mathematics. Jump to Navigation. UCB Mathematics Learn about the people and activities that make UC Berkeley one of the best places in the world for advanced research, graduate and undergraduate study in mathematics.

Spring Quantitative Reasoning Exam will be held Wed. Xinyi Yuan. Associate Professor. Number theory. Lin Lin. Numerical analysis; Quantum many-body problems; Quantum Erik Bates. NSF Postdoctoral Fellow. Probability theory, mathematical physics. Michael J. Probability theory, Combinatorics.

Edward Frenkel. Representation theory, Integrable systems, Mathematical Miller Research Fellow. Dispersive partial differential equations; water waves. Mina Aganagic. String theory. Gabriel Dorfsman-Hopkins. RTG Post-doctoral Scholar. Arithmetic geometry, p-adic geometry, mathematical Alan Hammond.

### About the Department

Statistical mechanics, studied rigorously via modern James Conway. Contact and symplectic geometry. James W. Numerical analysis, Applied control theory. Alexandru Scorpan. Visiting Scholar. Ryan A. Numerical analysis, medical imaging. Georgios Moschidis. General relativity, hyperbolic PDEs, differential geometry.

Dan-Virgil Voiculescu. Operator algebras, Hilbert space operators modulo normedA math circle is a social structure where participants engage in the depths and intricacies of mathematical thinking, propagate the culture of doing mathematics, and create knowledge.

To reach these goals, participants partake in problem-solving, mathematical modeling, the practice of art, and philosophical discourse. Some circles involve competition, others do not; all promote camaraderie. Math circles can have a variety of styles.

## Mathematical Sciences Research Institute

Some are very informal, with the learning proceeding through games, stories, or hands-on activities. Others are more traditional enrichment classes, but without formal examinations.

Some have a strong emphasis on preparing for olympiad competitions ; some avoid competition as much as possible. Models can use any combination of these techniques, depending on the audience, the mathematician, and the environment of the circle. Athletes have sports teams through which to deepen their involvement with sports; math circles can play a similar role for kids who like to think.

Two features all math circles have in common are 1 that they are composed of students who want to be there - they either like math, or want to like math, and 2 that they give students a social context in which to enjoy mathematics. Mathematical enrichment activities in the United States have been around since sometime beforein the form of residential summer programs, math contests, and local school-based programs.

Decisions about content are difficult for newly forming math circles and clubs, or for parents seeking groups for their children.

Project-based clubs may spend a few meetings building origami, developing a math trail in their town, or programming a mathy computer game together. Math-rich projects may be artistic, exploratory, applied to sciences, executable software-basedbusiness-oriented, or directed at real contributions to local communities.

Increasingly, math clubs invite remote participation of active people authors, community leaders, professionals through webinar and teleconferencing software. Problem-solving circles get together to pose and solve interesting, deep, meaningful math problems. Problems considered "good" are easy to pose, challenging to solve, require connections among several concepts and techniques, and lead to significant math ideas.

Best problem solving practices include meta-cognition managing memory and attentiongrouping problems by type and conceptual connections e. Guided exploration circles use self-discovery and the Socratic method to probe deep questions.

The book describes the classroom, organizational and practical issues the Kaplans faced in founding their Math Circle. The meetings encourage a free discussion of ideas; while the content is mathematically rigorous, the atmosphere is friendly and relaxed. The philosophy of the teachers is, " What you have been obliged to discover by yourself leaves a path in your mind which you can use again when the need arises " G.

Children are encouraged to ask exploratory questions.

## A Decade of the Berkeley Math Circle: The American Experience, Volume I

Are there numbers between numbers? What's a geometry like with no parallel lines? Can you tile a square with squares all of different sizes? Research mathematicians and connecting students with them can be a focus of math circles. Students in these circles appreciate and start to attain the very special way of thinking in research mathematics, such as generalizing problems, continue asking deeper questions, seeing similarities across different examples and so on.

Topic-centered clubs follow math themes, such as clock arithmetic, fractals, or linearity. Club members write and read essays, pose and solve problems, create and study definitions, build interesting example spaces, and investigate applications of their current topic. There are lists of time-tested, classic math club topics, especially rich in connections and accessible to a wide range of abilities.

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