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HU Credits:
20
Degree/Cycle:
1st degree (Bachelor)
Responsible Department:
Mathematics
Semester:
Yearly
Teaching Languages:
Hebrew
Campus:
E. Safra
Course/Module Coordinator:
Jake Solomon
Coordinator Office Hours:
Teaching Staff:
Prof. Jake Solomon,
Mr. Or Kedar
Course/Module description:
A comprehensive introduction to the foundations of analysis aimed at highly motivated students. Priority will be given to the most natural proof even if it is more challenging. An emphasis will be placed on multi-dimensional reasoning. Covers the material of Infinitesimal Calculus 1-3 in two semesters.
Course/Module aims:
To the learn the fundamental concepts and central theorems of mathematical analysis. To develop the skill of inventing proofs independently using these concepts and theorems.
Learning outcomes - On successful completion of this module, students should be able to:
By the end of the course, students will be able to understand mathematical proofs in analysis and to invent and write them independently.
Attendance requirements(%):
80
Teaching arrangement and method of instruction:
Lecture, written exercises
Course/Module Content:
Elementary set theory
The real numbers, axiomatic approach
n-dimensional Euclidean space
Metric spaces and topological spaces
Compactness
Connectedness
Sequences
Series
Continuity
The derivative a function of one variable, the mean value theorem, L'Hopital's theorem, Taylor's theorem, partial derivatives
The Riemann integral in arbitrary dimension, Lebesgue's theorem
The Riemann-Stieltjes integral, the fundamental theorem of calculus, integration by parts
Sequences and series of functions, the Arzela-Ascoli theorem, the Stone-Weierstrass theorem
The derivative of a function of several variables, the inverse function theorem
Properties of multidimensional integrals, Fubini's theorem, the change of variables theorem
Required Reading:
none
Additional Reading Material:
Rudin, Principles of Mathematical Analysis
Bartle, The Elements of Real Analysis, Second Edition
Munkres, Analysis on Manifolds
Grading Scheme :
Written Exam % 40
Submission assignments during the semester: Exercises / Essays / Audits / Reports / Forum / Simulation / others 20 %
Mid-terms exams 40 %
Additional information:
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