Mate1009: Algebra (Spring 2020)

Instructor: Mārtiņš Kālis
E-mail: martins@kalis.lv
Lectures: Wednesdays, 12.30–14.10, room 426 (auditorium 20)
Office hour: Tuesdays, 9.00-10.00, room 434

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, bc = 1, (ii) a = 1, bc = 0, (iii) a = 0, bc = 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) + 2.5P1 MT + 5P2
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