2022 S2 Algebra Assignments 
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Assignment 1  247 K 

2022 S2 Algebra Lecture Notes 
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Chapter 1: Introduction  257 K 
Chapter 2: Truth and Falsehood (complete)  300 K 
Chapter 3: Complex Numbers (complete)  271 K 
Chapter 4: Vectors (complete)  289 K 
Chapter 5: Matrices (complete)  321 K 
Chapter 6: Linear Transformations and Eigenvectors (complete)  225 K 

2022 S2 Algebra Lectures 
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Lecture 1 completed notes  652 K 
Lecture 1: Introduction (notation and sets)  228203 K 
Lecture 2 completed notes  866 K 
Lecture 2: Sets and Functions (complement of a set, recap of functions)  195034 K 
Lecture 3 completed notes  832 K 
Lecture 3: Propositional Logic (compound statements, truth tables, negating compound statements)  182512 K 
Lecture 4 completed notes  1171 K 
Lecture 4: Quantifiers (negating the implication, the universal and existential quantifiers, negating the universal quantifier)  192639 K 
Lecture 5 completed notes  498 K 
Lecture 6 completed notes  1210 K 
Lecture 6: Introduction to Proof (why do we need proof, common errors, basic proof strategies)  143511 K 
Lecture 7 completed notes  1468 K 
Lecture 7: Proof II (case by case proof, examples of proofs, prime numbers)  148034 K 
Lecture 8 completed notes  1489 K 
Lecture 8: Mathematical Induction (proof by induction, examples, general PMI)  128624 K 
Lecture 9 completed notes  1253 K 
Lecture 9: Complex Numbers (completed buses induction example, introduction to complex numbers, conjugate, modulus, division)  142511 K 
Lecture 10 completed notes  1187 K 
Lecture 10: Complex Numbers II (the complex plane, polar coordinates, Fundamental Theorem of Algebra, Euler's Identity)  121715 K 
Lecture 11 completed notes  965 K 
Lecture 11: Vector Revision (application of Euler's identity, vectors, adding/subtracting, dot product)  137346 K 
Lecture 12 completed notes  869 K 
Lecture 12: Vectors II (orthogonal vectors, properties of dot product, the cross product)  172758 K 
Lecture 13 completed notes  1069 K 
Lecture 13: Vectors II (properties of cross product, examples, length and angle, vectors with n components)  159302 K 
Lecture 14 completed notes  1212 K 
Lecture 14: Subspaces (definition and examples of subspaces, introduction to matrices)  162595 K 
Lecture 15 completed notes  742 K 
Lecture 15: Matrix Algebra Review (scalar multiples, matrix products, linear systems)  189651 K 
Lecture 16 completed notes  1062 K 
Lecture 16: Review of Gaussian Elimination  134741 K 
Lecture 17 completed notes  1276 K 
Lecture 17: The Matrix Inverse (Identity matrix, inverse, solving systems via inverse, matrix powers)  175070 K 
Lecture 18 completed notes  1696 K 
Lecture 18: Elementary Matrices (properties of inverse, elementary matrices and row operations)  184765 K 
Lecture 19 completed notes  1514 K 
Lecture 19: The Determinant (elementary matrices and the inverse, 2x2 determinant, basic properties)  184396 K 
Lecture 20 completed notes  1472 K 
Lecture 20: The Determinant II (3x3 and nxn determinants, computing determinants via row operations)  198864 K 
Lecture 21 completed notes  1044 K 
Lecture 21: Linear Transforms  173588 K 
Lecture 22 completed notes  1138 K 
Lecture 22: Eigenvectors (area and linear transforms, eigenvalues and eigenvectors)  180954 K 
Lecture 23 completed notes  2138 K 
Lecture 23: Finding Eigenvectors (Finding eigenvalues via characteristic equation, finding eigenvectors, matrix powers and eigenvectors)  151600 K 

2022 S2 Algebra Practice Test Questions 
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Practice Test Solutions  30667 K 
Test Study Guide  192 K 

2022 S2 Algebra Revision 
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Review of Algebra  949 K 
Review of Trigonometry  113 K 

2022 S2 Algebra Tutorial Exercises 
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Tutorial 1  92 K 
Tutorial 1: Solutions  105 K 
Tutorial 2  123 K 
Tutorial 2: Solutions  148 K 
Tutorial 3  101 K 
Tutorial 3: Solutions  161 K 

2022 S2 Course Information 
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Algebra Internal Assessment Schedule  76 K 
Algebra Lectures Zoom Details  71 K 
MATH140Info 2022  248 K 

Private Tutoring for 2022 
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Download the list of private tutors 