This is an introductory course in algebraic topology, which is the study of algebraic invariants of topological spaces. Topics covered include:singular homology, cell complexes and cellular homology, the Eilenberg-Steenrod axioms.

This is an introductory course in algebraic topology, which is the study of algebraic invariants of topological spaces. Topics covered include:singular homology, cell complexes and cellular homology, the Eilenberg-Steenrod axioms.

This is a continuation course to Algebraic Topology I. The course will cover more advanced topics in algebraic topology including:homology with coefficients, cohomology, homological algebra and universal coefficient theorems, Poincaré duality, ring structure of cohomology.

This is a continuation course to Algebraic Topology I. The course will cover more advanced topics in algebraic topology including:cohomology of spaces, operations in homology and cohomology, duality.

Introduction of mathematics as the universal language for scientific facts:The lecture aims on one hand at learning and exercising the mathematical trade and in the other hand at applying the learnt concept to medical, biological, chemical and mechanical problems.

Mathematics I covers mathematical concepts and techniques necessary to model, solve and discuss scientific problems - notably through ordinary differential equations.The main focus of Mathematics II is multivariable calculus.

Continuation of the topics of Mathematics I, with main focus on multivariable calculus.

Consolidation and extension of mathematics as the universal language for scientific facts:The lecture aims on one hand at learning and exercising the mathematical trade and in the other hand at applying the learnt concept to medical, biological, chemical and mechanical problems.

Continuation of the topics of Mathematics I, with main focus on multivariable calculus.

After a short review of algebraic topology we will study the basics of topological data analysis. This includes some coding exercises in javaplex. The second half of the seminar is concerned with applications of the methods learned in the first half.