Teaching

Algebra 1 for MSEM:

Latest posts:

# 18. Determinants and inverse matrices

# 17. Matrix of a linear map

# 16. Operations on matrices

# 15. Linear maps

# 14. Second test

# 13. Sums and intersections of subspaces

# 12. Describing a vector space

# 11. Vector spaces and linear combinations

# 10. Solving a system of linear equations

# 9. Fields

# 8. First test

# 7. Complex numbers

# 6. Orders

# 5. Equivalence relations

# 4. Comparing cardinalities of sets

# 3. Sums and intersections of families of sets

# 2. Families of sets, relations and functions

# 1. Mathematical notation and sets

Algebra 2 for MSEM:

Latest posts:

# 14. Linear programming

# 12. Bilinear spaces

# 13. Quadratic forms, polynomials and hypersurfaces

# 11. Dual space

# 10. Isometries, self-adjoint mappings and unitary spaces

# 9. Euclidean affine spaces

# 8. Euclidean spaces

# 7. Preparation for the test

# 6. Affine maps

# 5. Affine spaces

# 4. Jordan Theorem

# 3. Endomorphisms and their eigenvalues and eigenvectors

# 2. Groups

# 1. Rings

Elements of logic and set theory UKSW:

Latest posts:

# 12. Exam

# 11. Partial orders

# 10. Equivalence relations

# 9. Sets of cardinality continuum, comparing cardinality

# 8. Test

# 7. Countable sets

# 6. Sets of the same cardinality

# 5. Images and preimages

# 4. Indexed families

# 3. Functions

# 2. Families of sets and relations

# 1. Proving equality of sets

# 0. Mathematical notation

Information technology UKSW:

Latest posts:

# 1. Text processor

Introduction to mathematics UW:

Latest posts:

# 10. Partial orders

# 9. Equivalence relations

# 8. Sets of cardinality continuum

# 7. Countable sets

# 6. Sets of the same cardinality, comparing cardinality

# 5. Images and preimages

# 4. Indexed families

# 3. Functions

# 2. Families of sets and relations

# 1. Proving equality of sets

# 0. Mathematical notation

Linear algebra WNE UW:

Latest posts:

# 18. Exam preparation

# 17. Quadratic form

# 16. Linear programming

# 15. Third test

# 14. Affine subspaces of a linear space

# 13. Scalar product and perpendicularity

# 12. Eigenvalues and eigenvectors

# 11. Second test

# 10. Inverse matrix and Cramer’s rule

# 9. Determinants

# 8. Matrix of a linear map

# 6. Linear maps

# 7. Operations on matrices

# 5. First test

# 4. Describing a vector space

# 3. Vector spaces & linear combinations

# 2. Solving a system of linear equations

# 1. Introduction and polynomials

Linear algebra and geometry I UW:

Latest posts:

# 16. Endomorphisms and their eigenvalues and eigenvectors

# 15. Preparation for the second test

# 14. Inverse matrix and Cramer’s rule

# 13. Determinants

# 12. Quotient space and dual space

# 11. Matrix of a linear map

# 10. Operations on matrices

# 9. Linear maps

# 8. Preparation for the first test

# 7. Infinite dimensional spaces, sums and intersections

# 6. Describing a vector space

# 5. Vector spaces and linear combinations

# 4. Polynomials over a field

# 3. Complex numbers

# 2. Fields

# 1. Solving a system of linear equations

Linear algebra and geometry II UW:

Latest posts:

# 11. Euclidean affine spaces

# 10. Affine maps

# 9. Affine spaces

# 8. Unitary spaces

# 7. Isometries and self-adjoint mappings

# 6. Euclidean spaces

# 5. Preparation for the first test

# 4. Bilinear spaces

# 3. Jordan Theorem

# 2. Endomorphisms and their eigenvalues and eigenvectors

# 1. Revision and a short introduction to groups

Mathematical Analysis 2 WNE UW:

Latest posts:

# 13. Preparation for the exam

# 12. Applications of multidimensional integrals

# 11. Preparation for the second test

# 10. Multidimensional integrals

# 9. Extrema on manifolds

# 8. Diffeomorphisms and theorems of inverse and implicit function

# 7. Extrema

# 6. Preparation for the first test

# 5. Derivatives of multivariable functions

# 4. Sets, limits and continuity in multi-dimensional space

# 3. Norms, inner products and balls

# 2. Definite integral

# 1. Indefinite Integral

Mathematics 0, WCh UW:

Latest posts:

# 10. Definite Integral

# 9. Indefinite integral

# 8. Taylor’s formula and approximations

# 7. Analysis of a real function

# 6. Derivatives

# 5. Convergence and continuity of a function

# 4. Preparation for the first test

# 3. Mathematical induction, infimum, sumpremum and limits of sequences

# 2. Powers, logarithms and trigonometry

# 1. Memories from school

Mathematics, 2nd semester, WG UW:

Latest posts: