The Structure of Higher Mathematics
Budapest , Hungary
January, 2007

In January of 2009 the MSCS Department is offering Mathematics 234, “The Structure of Higher Mathematics” in Budapest, Hungary. This is a course with a prerequisite of Mathematics 220. (Linear Algebra) The course will count towards the mathematics major but you need not be a major to be in the class. This course is a good transition from calculus and linear algebra to the required theoretical courses, real analysis or abstract algebra. We study topics such as logic, set theory, relations the number system, functions, cardinality, and an introduction to the structures of real analysis and algebra. The class meets for 2 hours each morning and also some afternoons and there will be a mid-term and final exam. Students will be asked to keep a journal.

There are many advantages to having this course meet in Budapest . In the first place, Budapest is a beautiful, sophisticated city with rich traditions and culture. The Danube River separates the ancient cities of Buda and Pest . There are wonderful museums and theatres. There are concerts and recitals going on every night. On most nights in January there are two different operas being performed in the city. Furthermore, these things are very affordable. Traditional Hungarian food is available throughout the city at reasonable prices and is frequently accompanied by live gypsy music. We will also take a couple of weekend train trips to visit a few Hungarian towns other than Budapest . Budapest is also one of the world centers of mathematics. Hungary has produced many great mathematicians and we will meet a few of them and learn about others.

We will live together in a hotel. The rooms have private baths and kitchenettes, and are quite comfortable. Living together establishes a group dynamic which is impossible to obtain on campus. It makes life in and out of the classroom much more interesting and vital. We will, initially wander about the city as a group, until you feel comfortable getting around on your own. When you arrive you get a transportation pass which allows you to travel on all of the city busses, streetcars and subways without charge. This is a city of 2,000,000 people but it is very easy to get around because the public transportation is so good.

In addition to the regular mathematics classes, we will have a series of additional lectures and classes by Hungarian scholars. These will include a few introductory talks by some well known Hungarian mathematicians and presentations on the art, music, history and literature of Hungary . We will also have some beginning language instruction. Hungarian is a fascinating and difficult tongue.

Please contact Bruce Hanson or hansonb@stolaf.edu if you have any questions.

Text: “A Transition to Advanced Mathematics”, Smith, Eggen, & St. Andre

Jan. 2, Leave Minneapolis
Jan. 3, Arrive in Budapest
Jan. 4, Chapters 1.1, 1.2 Propositions, Connectives and Conditionals City Stroll
Jan. 5, Chapters 1.3, 1.4 Quantifiers, Proofs Language Class, Fallier Erika
Jan. 6, Chapters 1.5, 1.6 Proofs with Quantifiers
Jan. 7, Trip to Syntendre
Jan. 8, Chapters 2.1, 2.2 Sets and Set Operations, Language Class
Jan. 9, Chapters 2.3, 2.4, Indexed Sets, Induction, Language
Jan, 10, Chapter 2.5, 2.6, More Induction, Counting, Language
Class
Jan. 11, Trip to Pecs
Jan. 12, Chapters 3.1, 3.2 Relations
Jan. 13, Chapters 3.3, 4.1 Partitions, Functions
Jan. 14, Free Day
Jan.15, First Exam
Jan. 16, Chapters 4.2, 4.3, 1-1 and Onto Functions
Jan. 17, Chapter 4.4 Inage Sets, Arato Laszlo, 10:30am.
Jan. 18, Chapter 5.1, 5.2 Finite and Infinite Sets, Toth Baling, 10:30am
Jan. 19, Chapter 5.3 Countable Sets
Jan. 20-21, Free Weekend
Jan. 22, Chapter 5.4 Ordering Cardinal numbers, Halasz Peter (afternoon)
Jan. 23, Chapter 6.1 Algebraic Structures
Jan. 24, Chapters 6.2 Groups Laszcovitch Miklos, 10:30am
Jan. 25, Chapter 6.3 Subgroups
Jan. 26, Review
Jan. 27, Final Exam
Jan. 28, Fly Home

The class will meet for 2.5 hours per day. This will include a 15 minute break. There will be several special sessions which will include a walking tour of Budapest , 8 hours of language instruction, lectures on topics such as art, music and history, and two lectures given by eminent Hungarian mathematicians. Generally, our class will meet in the morning but we will move things around to accommodate our guest lecturers. Attendance at all classes and guest lectures is mandatory. Your grade will be based on the following components. You will be asked to keep a daily journal in which you will write about your observations and encounters with Hungarian Culture and you will be asked to turn in daily homework assignments. During the month you will be expected to visit at least five sites of significance and write brief reports on your visits. These sites will primarily be museums in and around the city.

Journal 5 pts
Sites of significance 5pts
Homework 10pts
1st Exam 30pts
Final 30pts or 50pts