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0th Prep Semester
0th Prep Semester
Lecture
Lecture
未命名
9.11
9.10 Matrices
9.9 Vectors and matrices
9.5 Polynomials
9.4 Polynomials
9.3 Polar form
9.2 Limit and complex number
8.29 Sequences and series
8.28 Completeness and density
8.27 Real numbers and completeness
8.26 Modular arithmetic
8.22 Divisibility
8.21 Induction
8.20 Counting with natural numbers and recursive definitions
8.19 Relation
8.15 Function
8.14 Sets
8.13 Quantifiers
8.12 Propositional logic
Tutorial
Tutorial
9.13
9.12 Matrices tutorial
9.11
9.10 Polynomials and Matrices Tutorial
9.6 Polynomials tutorial
9.5
9.4
9.3
8.30
8.29 Real numbers tutorial
8.28 Modular arithmetic tutorial
8.27 Divisibility tutorial
8.23 Induction tutorial
8.22 Counting with natural numbers Tutorial
8.20_21 Relation Tutorial
8.16 Function Tutorial
8.15 Sets Tutorial
8.14 Quantifiers Tutorial
8.13 Propositional logic tutorial
8.8 Mathematical Tutorial
1st Semester
1st Semester
Algebra A
Algebra A
Learning Log
Learning Log
11
10
9
8
7
6
5
4
3
2
1
Lecture
Lecture
1.6
12.31
12.30
12.24 Triangularizable Operators
12.23 Diagonalization
12.17 Further properties of det
12.16 The determinant
12.10 Polynomial
12.9 Change of basis
12.3 The dual space
12.2 Product spaces
11.26 Isomorphisms
11.25 Representing linear maps by matrices
11.19 Null space and range
11.18 Linear Maps
11.12 Linear Independence and Basis
11.11 Finite-Dimensional Vector Spaces
11.5 Solving matrices
11.4 Linear Equation
10.29 Subpaces
10.28 Subspaces
10.22 Linear combination
10.21 Vector Spaces
10.15 Matrices
10.14 Fields
Tutorial
Tutorial
1.10
1.8
1.3
12.27
12.25
12.20
12.18 Polynomial
12.13 Change basis
12.11 Annihilator
12.6 Dual space
12.4 Product sapce
11.29 Isomorphism
11.27 Representing linear maps by matrices
11.22 Null Space
11.20 Null space and range
11.15 Linear independent and basis
11.13 Finite-Dimensional Vector Spaces
11.6 Solving equation
11.1 Subspaces
10.30 Subspaces
10.25 Linear combination
10.23 Vector Spaces
10.18 Matrices
10.16 Fields
Workshop
Workshop
1.3
12.27
12.20
12.13 Change basis
12.6 Quotient space
11.29 Represent linear maps
11.22 Null space
11.15 Linear independent and basis
11.8 Solving equation
11.1 Subspaces
10.25 Vector spaces
10.18 Matrices
Basic Concepts in Mathematics
Basic Concepts in Mathematics
Lecture
Lecture
1.6
12.30 Infinite set
12.23
12.16 Cardinality
12.9 Function
12.2 Operation with functions
11.25 Total Order
11.18 Partition
11.11 Relation
11.4 Three Principles
10.28 Set
10.21 Proof
10.14 Propositions and Quantifiers
Tutorial
Tutorial
1.9
1.2
12.25
12.18 Cardinality
12.11 Function
12.4 Function
11.27 Function
11.20 Partition
11.13 Relation
11.6 Three principles
10.30 Set
10.23 Proof
10.16 Propositions and Quantifiers
Workshop
Workshop
1.2
12.25
12.18 Cardinality
12.11 Function
12.4 Functions
11.27 Total Order
11.20 Partition
11.13 Relation
11.6 Three principles
10.30 Set
10.23 Proof
10.16 Propositions and Quantifiers
INT. To Computer Science M
INT. To Computer Science M
Lab
Lab
12.27 Lab11
12.20 Lab10
12.13 Lab9
12.6 Lab8
11.29 Lab7
11.22 Lab6
11.10 Lab4
11.1 Lab3
10.25 Lab2
10.18 Lab1
Lecture
Lecture
1.6 time complexity
12.23 Some fundamental algorithms on sequences
12.16 Points
12.9 Functions
12.2 Arrays, random number generation
11.26 Programming style, command line arguments to main, advances console output
11.18 IO ASCII EOF
11.11 Statement, assignment operators, linear accumulation
11.4 Increments Short-Circuit Conditionals Loop Control
10.28 Logic Loops Conditions
10.21 Foundations of Programming and Process Management in Computing
10.14 Introduction
Tutorial
Tutorial
1.9
1.2 Tutorial 11
12.17 Tutorial10
12.11 Tutorial 9
12.5 Tutorial 8
11.28 Tutorial7
11.21 Tutorial6
11.14 Tutorial5
11.7 Tutorial4
10.31 Tutorial3
10.24 Tutorial2
10.17 Tutorial1
Infinitesimal Calculus 1
Infinitesimal Calculus 1
Lecture
Lecture
1.9
1.6
1.2
12.30 Taylor approximation
12.26
12.23 More theorems of derivates
12.19 Theorems of Derivative
12.16 Derivative of the inverse
12.12 Derivatives
12.9 Derivatives
12.5 Theorems of Continuity
12.2 Bolzano, Intermedia value theorem
11.28 Continuous Function
11.25 Continuous
11.18&21 Limit of functions
11.14 The exponential function
11.11 Series
11.7 Series
11.4 Cauchy sequences
10.31 Subsequences
10.28 Limit
10.24 Convergence
10.21 Supremum and the Completeness Axiom
10.17 Absolute value and Supremum
10.14 Axioms of real numbers
Tutorial
Tutorial
1.10
1.9
1.3
1.2
12.27
12.26
12.20
12.19
12.13 Derivative
12.12 Derivative
12.6 Bolzano, Intermedia value theorem
12.5 Bolzano theorem
11.29 Continuity of functions
11.28 Infinite limits
11.22 Sequential Limit
11.21 Limit of function
11.15 Topology
11.14 Series
11.8 Series
11.7 Sequence
11.1 Limit
10.31 Convergence
10.25 Supremum and the Completeness Axiom
10.24 Absolute value and Supremum
10.17 Axioms of real numbers
Workshop
Workshop
1.10
1.3
12.27
12.20
12.13 Derivative
12.6 Bolzano theorem
11.29 Limit of functions
11.22 Limit of function
11.15 Series
11.8 Cauchy sequences
11.1 Subsequences
10.25 Supremum and Infimum
10.18 Absolute value
2nd Semester
2nd Semester
Algebra A
Algebra A
Tutorial Note
Lecture Note
Algebra B
Algebra B
Lecture
Lecture
5.7 Inner Product
4.30 Inner Product
4.28 Jordan basis and form
4.9 Jordan Basis
4.8 Jordan Block and Basis
4.7 Introduction to Block Matrix
4.2 Proof of Cyclic Decomposition Theorem
3.31 Admissible subspaces
3.26 Companion matrix
3.24 Diagonal and nilpotent
3.19 Projector
3.17 Projections
3.12 Theorems of minimal polynomial
3.10 Invariant subspace
3.5 Minimal Polynomial
3.3 Revision and Notation of Diagonalization
Tutorial
Tutorial
5.8 Jordan Form
4.24 Jordan Form
4.10 Jordan Form
4.3 Cyclic Decomposition Theorem
3.27 Cyclic vector
3.20 Projector
3.13 Invariant
3.6 Diagonalization
Combinatorics
Combinatorics
Lecture
Lecture
4.28 Euler Tour and The Pigeonhole principle
4.23 Euler Walking
4.21 Graphs
4.7 Catalan and Generating Function
3.31 Recursive Formulas and Generating Functions
3.24 Stirling number formula
3.17 Bell Number
3.10 Counting maps
3.3 Counting
Tutorial
Tutorial
5.7 Euler Tour
4.30 Graph
4.9 Generating functions
4.2 Formal functions
3.26 Inclusive-Exclusive Principle
3.19 Stirling number
3.12 Binomial Coefficients
3.5 Counting
Infinitesimal Calculus 2
Infinitesimal Calculus 2
Lecture
Lecture
5.7 Partial derivatives, differentiation and the gradient
4.30 Limits and continuity on functions of 2 variables
4.28 Geometry and topology of the Euclidean space
4.23 Improper Integrals, comparison and ratio tests
4.21 Properties of improper integrals
4.9 Applications of the Riemann Integral
4.7 Integration techniques
4.2 Fundamental Theorem of Calculus
3.31 Integrable Limit theorem
3.26 The properties of Integral
3.24 Properties and examples of integrable functions
3.19 Riemann Sum
3.17 Approximation of Functions
3.12 Taylor’s Series
3.10 Power Series
3.5 Series
3.3 Sequences of functions
Tutorial
Tutorial
5.7 Metric Space
4.30 Improper Integral
4.9 Calculating Integral
4.2 Fundamental Theorem of Calculus
3.26 Integrable function
3.19 Taylor Series
3.12 Radius of Convergence
3.5 Sequence
Systems Programming
Systems Programming
Lecture
Lecture
5.11 Self 9.2
4.23 Self 8
4.28 Self 9
4.28 Lecture 9
Knowledge Supplement before Lecture 7
4.23 Lecture 8
4.21 Lecture 7
4.7 Lecture 6
3.31 Lecture 5
3.24 Lecture 4
3.17 Lecture 3
3.10 Lecture 2
3.3 Lecture 1
Tutorial
Tutorial
5.4 Tutorial 7-8
4.10 Tutorial 6
4.3 Tutorial 5
3.27 Tutorial 4
3.20 Tutorial 3
3.13 Tutorial 2
3.6 Tutorial 1
Career Lecture
Career Lecture
2024 数学系专场
IELTS Lecture 2025.3.6
Lecture Note
Algebra1_副本.pdf
