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MATH-120 · Summer 2026 · SSE Core

Linear Algebra with Differential Equations

The grammar of every linear system in mathematics — taught from the why, not just the how. From row reduction to abstract vector spaces, with proofs along the way.

Instructor
Imran Anwar
Credits
3ch · 4 lec/wk
Prereq
MATH-101
Text
Nicholson · Anton
Notes live
21 of 21
21 availableLecture Notesby weekPractice & Problem Sets7 · best 5 countQuizzesexams · weightsDates & Grading
01

Lecture Notes

Grouped by week. The current week is open by default — tap any week to expand.

Lec 1The Language of MatricesNicholson §1.1–1.2 · 8 Junopen →Lec 2Row Operations & Gaussian EliminationNicholson §1.2 · 9 Junopen →Lec 3RREF, Homogeneous Systems & Linear CombinationsNicholson §1.3 · 10 Junopen →Lec 4Solution Structure & ApplicationsNicholson §1.4 · 11 Junopen →
Lec 5Matrix Algebra: Addition, Scalar Multiplication & TransposeNicholson §2.1–2.2 · 15 Junopen →Lec 6The Inverse of a MatrixNicholson §2.4 · 16 Junopen →Lec 7Elementary Matrices & Solving SystemsNicholson §2.5 · 17 Junopen →Lec 8LU-Factorization & Input–Output ModelsNicholson §2.7–2.8 · 18 Junopen →
Lec 9Determinants: Cofactor Expansion & PropertiesNicholson §3.1 · 22 Junopen →Lec 10Determinants & Matrix InversesNicholson §3.2 · 23 Junopen →Lec 11Eigenvalues & EigenvectorsNicholson §3.3 · 24 Junopen →
Lec 12Diagonalization & Dynamical SystemsNicholson §3.3 · 29 Junopen →Lec 13Polynomial Interpolation & Linear RecurrencesNicholson §3.2 and §3.4 · 1 Julopen →Lec 14Subspaces and SpanningNicholson §5.1 · 2 Julopen →
Lec 15Basis & DimensionNicholson §5.2 · 6 Julopen →Lec 16Vector Spaces (Abstract)Nicholson §6.2–6.3 · 7 Julopen →Lec 17Extending a Basis; Row, Column & Null SpaceNicholson §6.4 · 8 Julopen →Lec 18Dot Product, Distance & Gram–SchmidtNicholson §5.3, §8.1 · 9 Julopen →
Lec 19Orthogonal Projections, Complements & Symmetric MatricesNicholson §8.1–8.2 · 13 Julopen →Lec 20Introduction to Linear TransformationsNicholson §2.6 · 14 Julopen →Lec 21Matrix of a Transformation; Kernel & RangeNicholson §2.6–7.2 · 15 Julopen →
02

Practice & Problem Sets

Practice problems, worked solutions, and the weekly problem set — one row per week.

WeekPractice ProblemsSolutionsProblem Set
W1Practice · soonSolutions ↗Problem Set · soon
W2Practice · soonSolutions · soonProblem Set · soon
W3Practice · soonSolutions · soonProblem Set · soon
W4Practice ↗Solutions ↗Problem Set · soon
W5Practice · soonSolutions · soonProblem Set · soon
W6Practice · soonSolutions · soonProblem Set · soon
W7Practice · soonSolutions · soonProblem Set · soon
03

Quizzes

Seven quizzes across the term · best 5 of 7 count. Papers and solutions post after each quiz.

1
Quiz 1
15 Jun · Mon
Solution ↗
2
Quiz 2
22 Jun · Mon
Solution ↗
3
Quiz 3
29 Jun · Mon
Solution ↗
4 & 5
Quiz 4 & 5
06 Jul · Mon
Solution ↗
6 & 7
Quiz 6 & 7
20 Jul · Mon
Solution · soon
04

Dates & Grading

Grade Weighting

Quizzes · best 5 of 730%
Midterm30%
Final · comprehensive40%

Exam Dates

Midterm03 Jul · 10:00 AMMidterm-Sol ↗Mock Exam ↗
Final25 Jul · 3:00 PMMidterm-Sol · soonMock Exam · soon
Two quizzes are dropped — best 5 of 7 count.
05

Teaching Team

Instructor & 4 TAs — office hours & contact
RoleNameEmailOfficeHours
InstructorImran Anwarimran.anwar@lums.edu.pk9-155A SSEMon–Thu 4:00–5:00
TAMuhammad Shoaib Khanshoaib.khan@lums.edu.pk9-155 SSEMon–Thu 1:00–2:00
TAAzhar Javedazhar.javed@lums.edu.pk9-155 SSETBA
TAAqsa Noreen22070005@lums.edu.pk9-155 SSETBA
TAHajra Mahmood28100096@lums.edu.pkMath LobbyMon/Wed/Thu 5–6 · Fri 4–5
06

Full Syllabus

Seven-week outline (Nicholson sections)
Week 1Systems of Linear EquationsCh 1
  • §1.2Row operations, echelon form & rank
  • §1.2Gaussian elimination
  • §1.3Homogeneous equations
  • §1.4Networks & chemical reactions
Week 2Matrix Algebra & FactorizationCh 2–3
  • §2.2–2.3Transpose, multiplication, inverses
  • §2.6–2.7LU factorization, input–output model
Week 3Determinants & DiagonalizationCh 3
  • §3.1–3.2Cofactor expansion, adjugate & inverse
  • §3.3Diagonalization, eigenvalues, dynamical systems
Week 4Vector Space ℝⁿCh 5–6
  • §6.1Vector space examples & properties
  • §5.1Subspaces, spanning, independence
  • §6.2–6.3Basis & dimension
Week 5Orthogonality & PolynomialsCh 8
  • §8.1Orthogonal bases (Gram–Schmidt)
  • §8.2Orthogonal diagonalization
  • §8.9Quadratic forms
Week 6Linear TransformationsCh 7 & 2
  • §7.1Transformation examples & properties
  • §2.5Matrix of a transformation
  • §7.2Kernel, image & dimension theorem
Week 7ApplicationsCh 10 & 8
  • §10.2Legendre interpolation
  • §8.10Differential equations via eigenvalues
07

Weekly Schedule

LectureTutorialOffice Hours
Mon
Tue
Wed
Thu
Fri
11:00am
12:00pm
1:00pm
2:00pm
3:00pm
4:00pm
5:00pm
6:00pm
7:00pm
Lecture
2:00pm–3:40pm
Acad-11
Shoaib · OH
12:30pm–1:30pm
9-155 SSE
Tutorial · Aqsa
11:00am–12:30pm
TBA
Hajra · OH
5:00pm–6:00pm
9-155 SSE
Lecture
2:00pm–3:40pm
Acad-11
Shoaib · OH
12:30pm–1:30pm
9-155 SSE
Lecture
2:00pm–3:40pm
Acad-11
Shoaib · OH
12:30pm–1:30pm
9-155 SSE
Hajra · OH
5:00pm–6:00pm
9-155 SSE
Lecture
2:00pm–3:40pm
Acad-11
Shoaib · OH
12:30pm–1:30pm
9-155 SSE
Tutorial · Azhar
4:00pm–5:00pm
TBA
Hajra · OH
5:00pm–6:00pm
9-155 SSE
Hajra · OH
4:00pm–5:00pm
9-155 SSE
Tutorial · Hajra
2:30pm–4:00pm
9-1C1 SSE
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