This course deals with the mathematics of high school advanced perspective. Its main purpose is to expose students to the future of how mathematicians see this profession, and thus prepare them to study mathematics at university.
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Learning mathematics at university is fundamentally different than learning mathematics at high school. This difference has many manifestations: at high school most of the learning focuses on the development of technical skills, and the tendency is to draw a clear separation between the various areas of mathematics. In contrast, the mathematics taught at university level deals to a large extent with mathematical structures and their interconnections.
This course is a "display window" of the mathematics that is being taught and studied at the university. Its main goal is to prepare would-be-students toward the mathematics that they will encounter, whether they choose to learn this subject, or any discipline that uses mathematics as its main language and tool (e.g., physics, computer science, and engineering).
Most of the mathematical content covered in this course is part of the high school curriculum. The difference is in the approach. In these lectures we will emphasize central mathematical concepts (e.g. the need to define ambiguous terms, and the principle of mathematical deduction). In particular, we will distinguish between deduction based on intuitive arguments and deduction based on rigorous reasoning. Moreover, we will demonstrate how seemingly distinct subjects merge to form the depth and beauty that are at the heart of the mathematical science.
The course will be given in Hebrew.
