This summer intensive in Berlin will introduce applied math majors to the theory and practice of complex analysis- in the very place where initial mathematics concepts were discovered! Berlin is home to numerous breakthroughs in mathematics and analysis. Euler, Weierstrass, Kronecker, as well as P´olya and Szeg˝o, the authors of the Math 191 textbook, lived, worked, and made discoveries in Berlin.
Students will not only explore the theory and practice of mathematics first-hand in class, they will be also be immersed in the historical context of the subject through excursions and visits to Berlin museums, Berlin Mathematical School and Humboldt Universität Berlin, where Weierstrass and other famous mathematicians actually worked.
• Explore Germany's capital city, recognized globally for its tumultuous past and multicultural present, rich with cafes, museums, and nightlife
• Immerse yourself in local culture through field trips to local museums and universities
• Study with local and international students at the Technische Universität Berlin, one of the most prestigious education institutions in Europe
Note that students will be housed in a nearby hotel without kitchens. However, there are affordable food options for students in the area.
Dates: May 19 – July 13, 2019
All dates are subject to change
Units: 7 units
Language of Instruction: English
Math 185: Introduction to Complex Analysis
Math 191: Experimental Courses in Mathematics
At least one year of college coursework completed by the start of the program
2.0 GPA or higher
Math 104 or equivalent are prerequisites
Application opens February 4, 2019
Space is limited and applications are accepted on a first-come, first-served basis
Deadline to apply is March 15, 2019
During the program, you will take two courses for a total of seven UC Berkeley units.
Course: Math 185
Title: Introduction to Analysis
Instructor: Olga Holtz
Units: 4 units
Prerequisites: Math 104, or equivalent
Math 185 is a core upper-division Math course focused on a rigorous introduction to complex analysis. It traditionally focuses on analytic functions of a complex variable. Main topics include Cauchy’s integral theorem, power series, Laurent series, singularities of analytic functions, the residue theorem with application to definite integrals. Some additional topics such as conformal mappings and various applications to other branches of mathematics as well as physics. Math 185 is often offered during the summer.
Math 185 will be taught using the traditional lecture format and teaching methods, using Visual Complex Functions, An Introduction with Phase Portraits, Birkhauser, by Elias Wegert, as the main textbook, and Complex Analysis, Springer-Verlag by T. W. Gamelin, as a supplementary text.
Notwithstanding the traditional lecture format, this version of Math 185 will be unusual in its unorthodox choice of material and its heavy reliance on visualization. In particular, both the main textbook and the lectures will often involve visual demonstrations using MATLAB and other software of phase portraits of functions, and ‘visual’ applications to various problems of mathematics and physics.
Course: Math 191
Title: Experimental Courses in Mathematics
Instructor: Olga Holtz
Units: 3 units
Prerequisites: Math 104, or equivalent
Math 191 is a variable topic upper-division Math class, where the selection of topics and teaching methods is made individually by a particular instructor. This class is often devoted to the art and science of problem-solving in Mathematics. One of the Math 191 versions each Fall is devoted to the preparation of the UC Berkeley Putnam team for the annual Putnam competition, the notoriously difficult North American contest in Mathematics.
Math 191 will be taught using a less traditional, intense problem solving (Socratic) method based upon the 2-volume book Problems and Theorems in Analysis, Springer-Verlag (1998) by George Polya and Gabor Szego.
Math 191 will be taught using a less traditional, intense problem solving (Socratic) method based upon the 2-volume book Problems and Theorems in Analysis, Springer-Verlag (1998) by George P´olya and Gabor Szeg˝o. It will serve as a companion course to Math 185 in that it will be devoted to solving fun and challenging problems in a complex analysis using problem-solving techniques developed by P´olya and Gabor Szeg˝o. It should be a unique experience.
The instructor has an extensive background in such problem-solving courses (Math H90, Math 191). In high school, college, and graduate school she took many problem-solving classes as a student and a top-ranked Math Olympiad winner herself. Later, her teaching of such problem-solving courses has been met with generally enthusiastic student response and earned her high teaching evaluation marks. In particular, she trained the Berkeley Putnam team to achieve some of the best team results in its history.
You can fulfill the L&S International Studies breadth requirement by full participation in a Berkeley Summer Abroad program. All of the required courses must be completed with a C-/P or better.
Summer Abroad staff will enroll you in courses after your acceptance to the program. Please make sure there are no active blocks on your student account that may impact your course enrollment.
Tuition and Program Fee
The fees to participate in this program are broken down into 1) tuition and 2) program fees, which are applied to your student billing account as follows:
2019 Fees UC Students Visiting Students Tuition (7 units) $2,933 $3,850 Program Fee $3,046 $3,046 Total Cost $5,979 $6,896
Fees are subject to change. All non-UC Berkeley students must pay an additional Document Management Fee of $58.
Estimated Out-of-Pocket Expenses
In addition to the fees outlined above, Berkeley Study Abroad has estimated costs for out-of-pocket expenses. These amounts are used to calculate financial aid packages for eligible students. Actual expenses will vary depending on your lifestyle and spending habits.
2019 Estimated Expenses Amount International Airfare and Transportation $1,336 Meals $1,432 Books $210 Personal Expenses (i.e. phone, passport, visa, etc.) $560 Total Estimated Out-Of-Pocket Expenses $3,538
Financial aid is available for Berkeley students who are enrolled in at least 6 units during the summer. All other students should contact the financial aid office at their home institution for more information.
Explanation of Fees
Tuition is based on a per unit cost:
• The UC undergraduate student rate is $419 per unit
• The visiting student rate for all non-UC participants is $550 per unit
The program fee includes* the following items:
• Housing for the full duration of the program. Students will be housed in a hotel nearby the Technical University Berlin and/or Berlin Mathematical School
• Excursions and program activities
• On-site orientation activities including an introduction to Berlin and placement, etc.
• Travel insurance to cover accident/sickness medical coverage, emergency medical evacuation, security extraction, and other travel assistance services
• Other program-related costs including fees for group transportation, guest lecturers, museum admissions, etc.
• The initial non-refundable deposit of $400, which is due at the time of application and is applied to the program fee
*Please note that the list of items included in the program fee is not all-inclusive and is subject to change.
The following items are excluded from the program fee:
• International airfare
• Personal expenses (souvenirs, routine medical expenses, toiletries, etc.)
• Course materials (textbooks and readers)
• Other travel expenses (passport, visa, etc.)
• Commuting costs for daily travel to and from classes (classes for this program are generally walking distance from the program housing)
Application opens February 4, 2019 Application closes March 15, 2019 Applicants notified of selection March 22, 2019 Deadline to confirm participation or cancel for a refund of all program-related fees, minus $400 deposit April 5, 2019 Attend pre-departure orientation* Late April-May Arrive in Berlin May 19, 2019 Last day of program† July 13, 2019
* These events take place on the UC Berkeley campus. If you are not on campus during this time, we will schedule a meeting via phone or Skype.
† Students are expected to check into program housing on May 19, 2019, and will be expected to check out of program housing on July 13, 2019. Students who arrive in-country early or depart after the last day may do so, but they are responsible for arranging their own accommodations outside of the program dates.
All dates are subject to change.
Olga Holtz, Ph.D.
Olga Holtz received her Diploma  in Applied Mathematics from Southern Ural State University in Chelyabinsk, Russia, and her Ph.D.  in Mathematics from the University of Wisconsin-Madison. She held a post-doctorate research position [2000-2002] at the Computer Science Department of the University of Wisconsin-Madison, a Humboldt fellowship [2002-2003] at the Institute of Mathematics of Technical University Berlin, a Morrey Assistant Professorship [2004-2007] and an Associate Professorship [2007-2010] at the Department of Mathematics of the University of California-Berkeley. Currently, Holtz is a Professor of Mathematics at the University of California-Berkeley. She has received a Sofja Kovalevskaja award , a European Mathematical Society Prize , an ERC Starting Grant , two Von Neumann Fellowships at the Institute for Advanced Study [2009, 2014], and an AMS Fellowship . Holtz is also an award-winning screenwriter and film director.
Berkeley Summer Abroad