Prof. Mikhail Katz

Time: sunday 14:00-17:00. Classroom Location in '24: Building 403, room 217.

syllabus for academic year '23-'24

Course notes: Infinitesimal analysis course notes in English

חוברת הקורס בּחשׁבּון אנפיניטסימלי
Lecture notes on infinitesimal calculus in Hebrew by Luie Jennings: part 1 (13 lectures, 81 pages), part 2 (13 lectures, 84 pages)

Homework for '24:
homework set 1 for '24 Due date: 19 may '24.
homework set 2 for '24 Due date: 2 june '24.
homework set 3 for '24 Due date: 16 june '24.
homework set 4 for '24 Due date: 30 june '24.
homework set 5 for '24 Due date: 7 july '24.
homework set 6 for '24 Due date: 14 july '24.

Syllabus:
1. The utrapower construction of the hyperreals
2. Enlarging sets and functions; transfer principle
3. Relational structures, *-transform, transfer
4. Transfer, Los, and arithmetic of hyperreals
5. Sequences, series, continuity
6. Uniform continuity and convergence, derivatives
7. Internal sets, external sets, and transfer
8. Defining internal sets, saturation
9. Saturation of internal sets, topology
10. Universes, strong transitivity
11. Superstructures
12. Advanced topics

Textbook: Goldblatt, Robert. Lectures on the hyperreals. An introduction to nonstandard analysis. Graduate Texts in Mathematics, 188. Springer-Verlag, New York, 1998.

Old exams: exam moed A '22 - exam moed B '22 - exam moed A '24 - exam moed B '24 -

Old Homework for '22: homework set 1 for '22, homework set 2 for '22, homework set 3 for '22, homework set 4 for '22, homework set 5 for '22.

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