Instructor: Mārtiņš Kālis

E-mail: martins@kalis.lv

Lectures: Wednesdays, 12.30–14.10, ~~room 426 (auditorium 20)~~ MS Teams

Office hour: Tuesdays, 9.00-10.00, ~~room 434~~ MS Teams

**Lecture **14 (13 May 2020). Polynomial roots and factors (p. 132–166) in lecture notes. The lecture will be recorded and available on MS Teams.

**Lecture **13 (6 May 2020). Basics of polynomials (up to and including polynomial division)

The lecture will be recorded and available on MS Teams.**Quiz #3** on complex numbers will take place at the beginning of lecture.

**Lecture **12 (29 April 2020). Complex numbers: Argument of complex numbers (5.6), De Moivre’s theorem (5.7).

The lecture will be recorded and available on MS Teams.**Quiz #3** on complex numbers will take place at the beginning of lecture 13, May 6, 12:30. Please let me know if you are not able to join at this time.

– Practice problems: problems 5, 6, 7, 8 from section 5.8.

Additional resources, useful to freshen up or catch up on the basics:

– Trigonometry fundamentals | Lockdown math ep. 2 | 3blue1brown

– Complex number fundamentals | Lockdown math ep. 3 | 3blue1brown

– More on e^iπ=-1 (this is outside of the scope of this course).

**Lecture **11 (22 April 2020). Complex numbers: complex conjugate (5.4), modulus of a complex number (5.5, up to, excluding Apollonius circles)

Please read sections 5.4 and 5.5 (up to, excluding Apollonius circles) from the lecture notes.

The lecture will be recorded and available on MS Teams.

– Practice problems: problems 5 (find just the modulus, not the principal argument), 9, from section 5.8.

**Lecture **10 (15 April 2020). Complex numbers.

If you are not familiar with complex numbers or need a refreshment, please watch the following video: Complex Numbers: Part Imaginary, but Really Simple by Dr. Strang.

Please read sections 5.2 and 5.3 from the lecture notes. Read 5.1 if you are curious.

– Practice problems: problems 1, 2, 3, 4 from section 5.8.

**Lecture **8 (25 March 2020) & **Lecture **9 (1 April 2020). Determinants.

– Practice problems: problems 4, 5, 8, 9, 11, 14 from section 4.1. (the other problems from the section are helpful, but optional).

Additional resources:

– Cramer’s Rule, Inverse Matrix, and Volume, MIT 18.06, Lectures 18, 19, 20

– “Linear algebra and its applications”, Gilbert Strang, chapter 4 (Determinants). available in the library.

**Midterm-homework.** The midterm graded homework replaces Quiz #2 and midterm exam scores for the final grade. The deadline for submissions ir 5 April 2020, 23:59.**Edit 2020-03-25**: 2(c) should read Solve A⃗x = b for (i) a = 1, ~~b~~**c** = 1, (ii) a = 1, ~~b~~**c** = 0, (iii) a = 0, ~~b~~**c** = 1.

**Lecture **7 (18 March 2020). **Independent study.** Please read sections 2.5 and 2.6, and do the practice problems below.

– Practice problems: problems 1, 3, 4, 9, 11, 13, 22 from section 2.7. (the other problems from the section are helpful, but optional).

Additional resources:

– 3blue1brown series “Essence of linear algebra“, episodes 6 & 7 (shared with lecture 6), episode 12.

– Projection Matrices and Least Squares, MIT 18.06, Lecture 16

– Cramer’s Rule, Inverse Matrix, and Volume, MIT 18.06, Lecture 20

– “Linear algebra and its applications”, Gilbert Strang, section 3.3. (Projections and least squares), available in the library.

**Lecture **6 (11 March 2020). Matrix recurrence relations (2.3), Non–singular matrices (2.5).

– Practice problems: problems 2–5 from section 2.4. (the other problems from the section are helpful, but optional).

Additional resources:

– 3blue1brown series “Essence of linear algebra“, episodes 6 & 7 (shared with lecture 7).

– Multiplication and Inverse Matrices, MIT 18.06, Lecture 3

– “Linear algebra and its applications”, Gilbert Strang, sections 1.6. (inverses and transposes), 2.2. (Solving Ax=0 and Ax=b), available in the library.

**Lecture **5 (4 March 2020). Matrices. Linear transformations.

– Practice problems: problem 1 from section 2.4

Additional resources:

– 3blue1brown series “Essence of linear algebra“, episodes 1–5.

– “Linear algebra and its applications”, Gilbert Strang, section 1.4., available in the library.

**Lecture **4 (26 Feb 2020). Field axioms. Matrices.

– Practice problems: 12, 13 (Chapater 1), example 2.1.2., problem 1 from section 2.4.

**Lecture 3** (19 Feb 2020). Homogeneus systems of equations. Arithmetic modulo p. Field axioms.

– Jupyter notebook from the lecture.

– Practice problems: 6, 7, 8, 9, 11 (Chapater 1)

– Optional: 14, 15, 16

Additional resources:

– Modular arithmetic on Khan Academy

– There will be a 30 minute quiz on Chapter 1 (except Field axioms) during the next lecture.

**Lecture 2** (12 Feb 2020). Gauss-Jordan method.

– Jupyter notebook from the lecture.

– Practice problems: 3, 4, 5 (Chapater 1)

Additional resources:

– Elimination with matrices, MIT 18.06, Lecture 2

– “Linear algebra and its applications”, Gilbert Strang, section 1.3., available in the library.

**Lecture 1** (5 Feb 2020). Introduction, (reduced-)row-echelon form, elementary row operations. Chapter 1 in course materials.

– Practice problems: 1, 2 (Chpater 1)

Additional resources:

– Column / row picture (will not be covered in depth), MIT 18.06, Lecture 1

– Elimination with matrices, MIT 18.06, Lecture 2

– “Linear algebra and its applications”, Gilbert Strang, section 1.3., available in the library.

**Exams**: There will be 4 quizes (M1a, ~~M1b,~~ M2a, M2b – out of 5), ~~1 midterm exam (P1 – out of 10)~~, 1 midterm graded homework (MT – out of 32) and 1 final exam (P2 – out of 10). You can retake the quizes and exams once. **Attendance bonus**: For each fully attended class, 1/4 bonus point will be received. (Maximum: 16/4 = 4 points)**Your grade** (out of 100) = bonus + 1.25(M1a+~~M1b~~+M2a+M2b) + ~~2.5~~*P1** MT + 5*P2

To pass the course, you must get at least ~~4 points~~ 40% in each — the midterm and the final exam.

## Course materials by Abuzer Yakaryilmaz

**Course materials:** download **Exam questions in 2019:** download **Exam questions in 2016:** download