Transition Math and Algebra with Geometry (ETMAG 23z)🔗

Timetable🔗

Activity  Group     Time            Place       Lecturer
Lecture   all       Mon.  8:15-10   162         Gabriel Pietrzkowski, PhD
Tutorial  101       Thu. 18:15-20   104         Tomasz Kostrzewa, PhD
Tutorial  102       Thu. 10:15-12   104         Tomasz Kostrzewa, PhD
Tutorial  103       Wed. 16:15-18     6         Michał Dymek

Content🔗

  1. Sets and functions: basic definitions and properties. "One-to-one" functions, "onto" functions and permutations. Function composition and inversion.

  2. Functions and graphs. Exponential and logarithmic functions. Inverse trigonometric functions.

  3. Complex numbers: definition and properties. Polynomials over the field of real and complex numbers. Remainder theorem. Roots of polynomials. Main Theorem of Algebra.

  4. Matrices: basic definitions and properties. Matrix operations: addition, scaling, multiplication, transposition. Square matrices, symmetric matrices.

  5. Determinant of a matrix: definition and properties. Rank of a matrix.

  6. System of linear equations: General and homogeneous systems. Matrix form of a system of linear equations. Cramer's rule. Kronecker-Capelli theorem. Gauss elimination.

  7. Nonsingular matrices: matrix inversion.

  8. Vector spaces: basic definitions. Examples of vector spaces over the field of real and complex numbers. Subspaces: definitions and properties. Linear independence of a finite set of vectors in finite dimensional vector spaces. Basis and dimension of a vector space: definition and properties. Solution space of a system of linear equations.

  9. Axioms for real numbers. Sequences. Arithmetic and geometric sequences. Monotonicity and boundedness of a sequence. Convergence and divergence. Properties of the limit.

  10. Basic convergent sequences. The number e. Evaluating limits.

  11. Limits: one-sided limits and limits at infinity; continuity, theorems on continuous functions; extreme values.

  12. Derivatives: definitions, physical and geometric interpretation. Rolle's theorem. Lagrange's theorem. Cauchy's theorem.

  13. Evaluation of derivatives. Applications of derivatives. De l'Hospital rule.

  14. Derivatives of higher order: graphing functions using y' and y''. Monotonicity and convexity.

Textbooks🔗

  1. S. Lipschutz, M. Lipson: Schaum`s Outline of Linear Algebra, McGraw-Hill; 6rd edition (2017)

  2. Joel R. Hass, Christopher E. Heil, Maurice D. Weir: Thomas' calculus, Pearson; 14th edition (2018).

  3. ED. Bloch, The real numbers and real analysis. Springer Science & Business Media (2011)

Rules of the course🔗

Rules during tutorial classes🔗

  1. Each student can score from 0 to 40 points as a sum of:

    • 0 to 8 points for classroom activity;
    • 0 to 16 points for a midterm test on 6th tutorial class;
    • 0 to 16 points for a midterm test on 13th tutorial class.

  2. Specific rules for classroom activity scores will be established by tutorial classes lecturers.

  3. It is obligatory to attend tutorial classes.

  4. In order to justify the absence, a student must obtain a sick leave. 4 unexcused absences are allowed without consequences during the semester. Otherwise, 0 points is scored for classroom activity.

Rules during midterm tests🔗

  1. Each test will be held during tutorial classes and lasted 75 minutes.

  2. Each test will consist of several problems similar to problems solved during classes.

  3. In justified cases, the test dates may be changed by its organizer.

  4. A student is obliged to bring his student ID card (or another document proving his identity)

  5. You can use the same aids at the test as at the exam.

  6. Solutions should be written on A4 sheets or official paper. On each sheet of paper, in the upper left corner type in with CAPITAL LETTERS: your name, surname, index number, group number, initials of the tutor.

  7. Cheating is strictly forbidden.

  8. Leaving the test room without giving the test work back results in a score of 0 points for a given test. There is no possibility continuing the test, after leaving and returning to the room.

  9. In the case of absence justified by a sick leave, a student has the right to write a test at a different date. About the situation inform (just send an e-mail) the teacher who conducts the test within 3 days from the date of the test.

  10. A student breaking any of the above rules results in a score of 0 points for a given test.

  11. The results will be published within 2 weeks of the given test.

  12. A student has the right to read the assessed work.

  13. It is not possible to retake the test.

Rules during final exam🔗

  1. The written exam is graded on a scale of 0-60 points.

  2. The exam will consist of problems, in which the solution and the final results will be scored.

  3. A student is obliged to bring his student ID card (or another document proving his identity).

  4. A student may use a note written by his own on one A4 sheet paper (it cannot be a photocopy or a printout). You can write down information that you find helpful during the exam, however, you cannot post solutions to problems! On the sheet, in the upper left corner type in with CAPITAL LETTERS: your name, surname, index number.

  5. No technical aids can be used. In particular, a student is required to turn off all communication devices; cannot use calculators or other calculating devices.

  6. Solutions should be written on A4 sheets or official paper. On each sheet of paper, in the upper left corner type in with CAPITAL LETTERS: your name, surname, index number, group number, initials of the tutor.

  7. Cheating is strictly forbidden.

  8. Leaving the exam room without giving the test work back results in a score of 0 points for a given exam. There is no possibility continuing the exam, after leaving and returning to the room.

  9. A student breaking any of the above rules results in a score of 0 points for a given exam and failing the course.

  10. Results will be published within 1 week of the given exam.

  11. A student has the right to read the assessed work.

Final grade🔗

  1. A student has the right to take the examination on two dates during the winter examination session and on one date durin the fall examination session.

  2. If the examiner deems it necessary, the written exam may be supplemented with oral examination in order to determine the final number of points.

  3. To receive a positive grade, a student must obtain more than 30 points in one of the executed exams!

  4. The final grade is determined on the basis of the sum of in-semester points (0-40) and the last written exam points (0-60). It is calculated according to the following table:

Score: [0;50] (50;60] (60;70] (70;80] (80;90] (90;100]
Grade: 2 3 3,5 4 4,5 5
Fail Satisfactory Fair Good Very Good Excellent

Additional rules for distance learning🔗

  1. Provided that the mid-term test or one of the final exams will not be possible to conduct in a classroom, it will be held remotely. Details will be announced if the situation arises.

Lecture notes🔗

Lecture notes Theoretical part Solutions of exercises Tutorial class
Symbols Suite 1
Basic set theory Lecture 1 Theory 1 Solutions 1 Suite 2
Functions Lecture 2 Theory 2 Solutions 2 Suite 3
Complex numbers Lecture 3 Theory 3 Solutions 3 Suite 4
Polynomials Lecture 4 Theory 4 Solutions 4 Suite 5
Midterm test
Matrices Lecture 5 Theory 5 Solutions 5 Suite 6
Systems of Linear Equations Lecture 6 Theory 6 Solutions 6 Suite 7
Matrices: Invertability Lecture 7 Theory 7 Solutions 7 Suite 8
Vector spaces Lecture 8 Theory 8 Solutions 8 Suite 9
Sequences Lecture 9 Theory 9 Solutions 9 Suite 10
Limits of functions Lecture 10 Theory 10 Solutions 10 Suite 11
Midterm test
Continuous functions Lecture 11 Theory 11 Solutions 11
Differentiable functions Lecture 12 Theory 12 Solutions 12 Suite 12
Applications of differtiability Lecture 13 Theory 13 Solutions 13 Suite 13
Convexity and Graph Lecture 14 Theory 14 Solutions 14