Learning Notes

Learning note category

Mathematics

93 items

Mathematics Summary

8 items

Illustrated Summaries

6 items

Mathematics Summary · Illustrated Summaries

01 Common Methods for Finding Limits

Postgraduate Entrance Exam Mathematics Study Notes: 01 Common Methods for Finding Limits. Keep original formulas, diagrams, and example problems.

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Mathematics Summary · Illustrated Summaries

02 Differentiation Rules

Graduate Entrance Examination Mathematics study notes: 02 Differentiation Rules. Original formulas, diagrams, and examples are retained.

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Mathematics Summary · Illustrated Summaries

03 Differentiability, Continuity, and the Existence of a Differential

Graduate Entrance Examination Mathematics study notes: 03 Differentiability, Continuity, and the Existence of a Differential. Original formulas, diagrams, and examples are retained.

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Mathematics Summary · Illustrated Summaries

04 The Three Mean Value Theorems

Graduate Entrance Examination Mathematics study notes: 04 The Three Mean Value Theorems. Original formulas, diagrams, and examples are retained.

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Mathematics Summary · Illustrated Summaries

05 Linear Algebra - Eigenvalues and eigenvectors

Postgraduate Entrance Exam Mathematics Study Notes: 05 Linear Algebra - Eigenvalues and Eigenvectors. Retain original formulas, diagrams, and example problems.

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Mathematics Summary · Illustrated Summaries

06 Linear Algebra - Similar Diagonalization

Postgraduate Entrance Exam Mathematics Study Notes: 06 Linear Algebra - Similar Diagonalization. Retain original formulas, diagrams, and example problems.

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Formula Collection

2 items

Mathematics Summary · Formula Collection2026-07-29

Advanced Mathematics - Collection of Formulas

Postgraduate Entrance Exam Mathematics Study Notes: Advanced Mathematics - Formula Collection. Original formulas, diagrams, and example problems are retained.

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Mathematics Summary · Formula Collection

Advanced Mathematics - Mind Map

Postgraduate Entrance Exam Mathematics Study Notes: Advanced Mathematics - Mind Map. Original formulas, diagrams, and example problems are retained.

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Advanced Mathematics

61 items

Functions, Limits, and Continuity

15 items

Advanced Mathematics · Functions, Limits, and Continuity2024-02-26

Lecture 1: Course Outline

Postgraduate Entrance Exam Mathematics Study Notes: Lecture 1: Course Outline. Original formulas, diagrams, and example problems are retained.

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Advanced Mathematics · Functions, Limits, and Continuity2024-02-26

Lecture 2: Concepts of functions and common functions

Postgraduate Entrance Exam Mathematics Study Notes: Lecture 2: Concepts of Functions and Common Functions. Original formulas, diagrams, and example problems are retained.

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Advanced Mathematics · Functions, Limits, and Continuity2024-02-26

Lecture 3: Properties of functions

Postgraduate Entrance Exam Mathematics Study Notes: Lecture 3: Properties of Functions. Retain original formulas, diagrams, and example problems.

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Advanced Mathematics · Functions, Limits, and Continuity2024-02-28

Lecture 4: Foundations of Limits

Graduate Entrance Examination Mathematics study notes: Lecture 4: Foundations of Limits. Original formulas, diagrams, and examples are retained.

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Advanced Mathematics · Functions, Limits, and Continuity2024-02-29

Lecture 5: The concept of function limits

Postgraduate Entrance Exam Mathematics Study Notes: Lecture 5: The Concept of Function Limits. Retain original formulas, diagrams, and example problems.

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Advanced Mathematics · Functions, Limits, and Continuity2024-02-28

Lecture 6: Properties of Function Limits

Postgraduate Entrance Exam Mathematics Study Notes: Lecture 6: Properties of Function Limits. Retain original formulas, diagrams, and example problems.

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Advanced Mathematics · Functions, Limits, and Continuity2024-03-01

Lecture 7: Criteria for the Existence of a Limit

Graduate Entrance Examination Mathematics study notes: Lecture 7: Criteria for the Existence of a Limit. Original formulas, diagrams, and examples are retained.

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Advanced Mathematics · Functions, Limits, and Continuity2024-03-01

Lecture 8: Infinitesimals and Infinite Quantities

Graduate Entrance Examination Mathematics study notes: Lecture 8: Infinitesimals and Infinite Quantities. Original formulas, diagrams, and examples are retained.

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Advanced Mathematics · Functions, Limits, and Continuity2024-03-04

Lecture 9: Limits — Concepts, Properties, and Existence Criteria

Graduate Entrance Examination Mathematics study notes: Lecture 9: Limits — Concepts, Properties, and Existence Criteria. Original formulas, diagrams, and examples are retained.

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Advanced Mathematics · Functions, Limits, and Continuity2024-03-04

Lecture 10: Finding Limits

Postgraduate Entrance Exam Mathematics Study Notes: Lecture 10: Finding Limits. Retain original formulas, diagrams, and example problems.

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Advanced Mathematics · Functions, Limits, and Continuity2024-03-11

Lecture 11: Comparing Orders of Infinitesimals

Graduate Entrance Examination Mathematics study notes: Lecture 11: Comparing Orders of Infinitesimals. Original formulas, diagrams, and examples are retained.

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Advanced Mathematics · Functions, Limits, and Continuity2024-03-11

Lecture 12: Continuity of functions

Postgraduate Entrance Exam Mathematics Study Notes: Lecture 12: Continuity of Functions. Retain original formulas, diagrams, and example problems.

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Advanced Mathematics · Functions, Limits, and Continuity2024-03-11

Lecture 13: Points of Discontinuity and Their Classification

Graduate Entrance Examination Mathematics study notes: Lecture 13: Points of Discontinuity and Their Classification. Original formulas, diagrams, and examples are retained.

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Advanced Mathematics · Functions, Limits, and Continuity2024-03-11

Lecture 14: Operations and properties of continuity

Postgraduate Entrance Exam Mathematics Study Notes: Lecture 14: Operations and Properties of Continuity. Retain original formulas, diagrams, and example problems.

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Advanced Mathematics · Functions, Limits, and Continuity2024-03-11

Lecture 15: Properties of continuous functions on closed intervals

Postgraduate Entrance Exam Mathematics Study Notes: Lecture 15: Properties of Continuous Functions on Closed Intervals. Retain original formulas, diagrams, and example problems.

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Derivatives and Differentials

5 items

Advanced Mathematics · Derivatives and Differentials2023-12-13

Lecture 16: Basic Concepts of Derivatives

Postgraduate Entrance Exam Mathematics Study Notes: Lecture 16: Basic Concepts of Derivatives. Retain original formulas, diagrams, and example problems.

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Advanced Mathematics · Derivatives and Differentials2023-12-17

Lecture 17: Differentiation Rules

Graduate Entrance Examination Mathematics study notes: Lecture 17: Differentiation Rules. Original formulas, diagrams, and examples are retained.

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Advanced Mathematics · Derivatives and Differentials2023-12-18

Lecture 18: Higher-Order Derivatives

Graduate Entrance Examination Mathematics study notes: Lecture 18: Higher-Order Derivatives. Original formulas, diagrams, and examples are retained.

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Advanced Mathematics · Derivatives and Differentials2023-12-21

Lecture 19: Implicit Functions and Parametric Equations

Postgraduate Entrance Exam Mathematics Study Notes: Lecture 19: Implicit Functions and Parametric Equations. Original formulas, diagrams, and example problems are retained.

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Advanced Mathematics · Derivatives and Differentials2023-12-22

Lecture 20: Differentials of Functions

Graduate Entrance Examination Mathematics study notes: Lecture 20: Differentials of Functions. Original formulas, diagrams, and examples are retained.

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Mean Value Theorems and Applications of Derivatives

7 items

Advanced Mathematics · Mean Value Theorems and Applications of Derivatives2024-03-22

Lecture 21: Differential Mean Value Theorems

Graduate Entrance Examination Mathematics study notes: Lecture 21: Differential Mean Value Theorems. Original formulas, diagrams, and examples are retained.

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Advanced Mathematics · Mean Value Theorems and Applications of Derivatives2023-12-27

Lecture 22: L’Hôpital’s Rule

Graduate Entrance Examination Mathematics study notes: Lecture 22: L’Hôpital’s Rule. Original formulas, diagrams, and examples are retained.

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Advanced Mathematics · Mean Value Theorems and Applications of Derivatives2024-01-12

Lecture 23: Taylor's Formula

Postgraduate Entrance Exam Mathematics Study Notes: Lecture 23: Taylor's Formula. Original formulas, illustrations, and example problems are retained.

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Advanced Mathematics · Mean Value Theorems and Applications of Derivatives2024-01-13

Lecture 24: Monotonicity, Convexity, and Inflection Points

Postgraduate Entrance Exam Mathematics study notes: Lecture 24: Monotonicity, Convexity, and Inflection Points. Original formulas, diagrams, and examples are retained.

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Advanced Mathematics · Mean Value Theorems and Applications of Derivatives2024-01-14

Lecture 25: Local and Absolute Extrema of Functions

Graduate Entrance Examination Mathematics study notes: Lecture 25: Local and Absolute Extrema of Functions. Original formulas, diagrams, and examples are retained.

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Advanced Mathematics · Mean Value Theorems and Applications of Derivatives2024-01-15

Lecture 26: Drawing Function Graphs

Postgraduate Entrance Exam Mathematics Study Notes: Lecture 26: Drawing Function Graphs. Retain original formulas, diagrams, and example problems.

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Advanced Mathematics · Mean Value Theorems and Applications of Derivatives2024-01-15

Lecture 27: Indefinite Integrals and Integration by Substitution

Graduate Entrance Examination Mathematics study notes: Lecture 27: Indefinite Integrals and Integration by Substitution. Original formulas, diagrams, and examples are retained.

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Indefinite Integrals

3 items

Advanced Mathematics · Indefinite Integrals2024-01-17

Lecture 28: Indefinite integrals

Postgraduate Entrance Exam Mathematics Study Notes: Lecture 28: Indefinite Integrals. Original formulas, diagrams, and example problems are retained.

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Advanced Mathematics · Indefinite Integrals2024-01-17

Lecture 29: Integration by Substitution

Graduate Entrance Examination Mathematics study notes: Lecture 29: Integration by Substitution. Original formulas, diagrams, and examples are retained.

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Advanced Mathematics · Indefinite Integrals2024-01-19

Lecture 30: Integration by Parts

Postgraduate Entrance Exam Mathematics Study Notes: Lecture 30: Integration by Parts. Original formulas, diagrams, and example problems are retained.

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Definite and Improper Integrals

4 items

Advanced Mathematics · Definite and Improper Integrals2024-01-21

Lecture 31: Basic Concepts of Definite Integrals

Postgraduate Entrance Exam Mathematics Study Notes: Lecture 31: Basic Concepts of Definite Integrals. Original formulas, diagrams, and example problems are retained.

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Advanced Mathematics · Definite and Improper Integrals2024-01-23

Lecture 32: Calculation of definite integrals

Postgraduate Entrance Exam Mathematics Study Notes: Lecture 32: Calculation of Definite Integrals. Retain the original formulas, diagrams, and example problems.

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Advanced Mathematics · Definite and Improper Integrals2024-01-24

Lecture 33: Applications of Definite Integrals

Postgraduate Entrance Exam Mathematics Study Notes: Lecture 33: Application of Definite Integrals. Retain original formulas, diagrams, and example problems.

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Advanced Mathematics · Definite and Improper Integrals2024-01-24

Lecture 34: Application of Definite Integrals

Postgraduate Entrance Exam Mathematics Study Notes: Lecture 34: Application of Definite Integrals. Retain original formulas, diagrams, and example problems.

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Differential Equations

6 items

Advanced Mathematics · Differential Equations2024-02-01

Lecture 35: Basic Concepts of Differential Equations

Postgraduate Entrance Exam Mathematics Study Notes: Lecture 35: Basic Concepts of Differential Equations. Original formulas, diagrams, and example problems are retained.

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Advanced Mathematics · Differential Equations2024-02-01

Lecture 36: First-Order Linear Differential Equations

Postgraduate Entrance Exam Mathematics Study Notes: Lecture 36: First-Order Linear Differential Equations. Original formulas, diagrams, and example problems are retained.

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Advanced Mathematics · Differential Equations

Lecture 37: Order-Reducible Equations and Higher-Order Linear Differential Equations

Graduate Entrance Examination Mathematics study notes: Lecture 37: Order-Reducible Equations and Higher-Order Linear Differential Equations. Original formulas, diagrams, and examples are retained.

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Advanced Mathematics · Differential Equations2024-02-01

Lecture 37: Homogeneous Linear Differential Equations with Constant Coefficients

Postgraduate Entrance Exam Mathematics Study Notes: Lecture 37: Homogeneous Differential Equations with Constant Coefficients. Retain the original formulas, diagrams, and example problems.

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Advanced Mathematics · Differential Equations2024-02-02

Lecture 38: Constant Coefficient Nonhomogeneous Linear Differential Equations

Postgraduate Entrance Exam Mathematics Study Notes: Lecture 38: Nonhomogeneous Linear Differential Equations with Constant Coefficients. Original formulas, diagrams, and example problems are retained.

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Advanced Mathematics · Differential Equations

Lecture 40: Euler’s Equation

Graduate Entrance Examination Mathematics study notes: Lecture 40: Euler’s Equation. Original formulas, diagrams, and examples are retained.

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Multivariable Differential Calculus

3 items

Advanced Mathematics · Multivariable Differential Calculus2024-02-03

Lecture 40: Differentiation Rules for Multivariable Composite Functions

Graduate Entrance Examination Mathematics study notes: Lecture 40: Differentiation Rules for Multivariable Composite Functions. Original formulas, diagrams, and examples are retained.

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Advanced Mathematics · Multivariable Differential Calculus2024-02-07

Lecture 41: Differentiation of Implicit Functions

Graduate Entrance Examination Mathematics study notes: Lecture 41: Differentiation of Implicit Functions. Original formulas, diagrams, and examples are retained.

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Advanced Mathematics · Multivariable Differential Calculus2024-02-07

Lecture 43: Local and Absolute Extrema of Multivariable Functions

Graduate Entrance Examination Mathematics study notes: Lecture 43: Local and Absolute Extrema of Multivariable Functions. Original formulas, diagrams, and examples are retained.

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Multiple Integrals

3 items

Advanced Mathematics · Multiple Integrals2024-02-08

Lecture 44: Double Integrals

Postgraduate Entrance Exam Mathematics Study Notes: Lecture 44: Double Integrals. Original formulas, diagrams, and example problems are retained.

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Advanced Mathematics · Multiple Integrals2024-02-09

Lecture 45: Calculation of Double Integrals

Postgraduate Entrance Exam Mathematics Study Notes: Lecture 45: Calculation of Double Integrals. Retain original formulas, diagrams, and example problems.

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Advanced Mathematics · Multiple Integrals2024-02-09

Lecture 47: Triple Integral

Postgraduate Entrance Exam Mathematics Study Notes: Lecture 47: Triple Integrals. Original formulas, diagrams, and example problems are retained.

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Infinite Series

6 items

Advanced Mathematics · Infinite Series2024-02-12

Lecture 53: Series of Constants

Graduate Entrance Examination Mathematics study notes: Lecture 53: Series of Constants. Original formulas, diagrams, and examples are retained.

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Advanced Mathematics · Infinite Series2024-02-13

Lecture 48: Series of Positive Terms

Graduate Entrance Examination Mathematics study notes: Lecture 48: Series of Positive Terms. Original formulas, diagrams, and examples are retained.

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Advanced Mathematics · Infinite Series2024-02-14

Lecture 55: Alternating Series

Graduate Entrance Examination Mathematics study notes: Lecture 55: Alternating Series. Original formulas, diagrams, and examples are retained.

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Advanced Mathematics · Infinite Series2024-02-14

Lecture 56: Power Series

Postgraduate Entrance Exam Mathematics Study Notes: Lecture 56: Power Series. Original formulas, diagrams, and example problems are retained.

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Advanced Mathematics · Infinite Series2024-02-15

Lecture 51: Expanding Functions into Power Series

Postgraduate Entrance Exam Mathematics study notes: Lecture 51: Expanding Functions into Power Series. Original formulas, diagrams, and examples are retained.

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Advanced Mathematics · Infinite Series2024-05-16

Lecture 52: Fourier series

Postgraduate Entrance Exam Mathematics Study Notes: Lecture 52: Fourier Series. Retain original formulas, diagrams, and example problems.

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Vector Algebra and Analytic Geometry in Space

4 items

Advanced Mathematics · Vector Algebra and Analytic Geometry in Space

Lecture 53: Vector Algebra

Postgraduate Entrance Exam Mathematics Study Notes: Lecture 53: Vector Algebra. Original formulas, diagrams, and example problems are retained.

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Advanced Mathematics · Vector Algebra and Analytic Geometry in Space

Lecture 54: Planes and Lines in Space

Graduate Entrance Examination Mathematics study notes: Lecture 54: Planes and Lines in Space. Original formulas, diagrams, and examples are retained.

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Advanced Mathematics · Vector Algebra and Analytic Geometry in Space

Lecture 55: Surfaces and Space Curves

Postgraduate Entrance Exam Mathematics Study Notes: Lecture 55: Surfaces and Space Curves. Retain original formulas, diagrams, and example problems.

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Advanced Mathematics · Vector Algebra and Analytic Geometry in Space

Lecture 56: Geometric Applications of Multivariable Differentials

Graduate Entrance Examination Mathematics study notes: Lecture 56: Geometric Applications of Multivariable Differentials. Original formulas, diagrams, and examples are retained.

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Multivariable Integral Calculus and Applications

5 items

Advanced Mathematics · Multivariable Integral Calculus and Applications2024-02-11

Lecture 48: Line Integrals with Respect to Arc Length

Graduate Entrance Examination Mathematics study notes: Lecture 48: Line Integrals with Respect to Arc Length. Original formulas, diagrams, and examples are retained.

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Advanced Mathematics · Multivariable Integral Calculus and Applications2024-02-11

Lecture 49: Line Integrals with Respect to Coordinates

Graduate Entrance Examination Mathematics study notes: Lecture 49: Line Integrals with Respect to Coordinates. Original formulas, diagrams, and examples are retained.

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Advanced Mathematics · Multivariable Integral Calculus and Applications2024-02-12

Lecture 51: Surface Integrals with Respect to Area

Graduate Entrance Examination Mathematics study notes: Lecture 51: Surface Integrals with Respect to Area. Original formulas, diagrams, and examples are retained.

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Advanced Mathematics · Multivariable Integral Calculus and Applications2024-02-12

Lecture 52: Surface Integrals with Respect to Coordinates

Graduate Entrance Examination Mathematics study notes: Lecture 52: Surface Integrals with Respect to Coordinates. Original formulas, diagrams, and examples are retained.

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Advanced Mathematics · Multivariable Integral Calculus and Applications

Lecture 61: Introduction to Vector Fields

Graduate Entrance Examination Mathematics study notes: Lecture 61: Introduction to Vector Fields. Original formulas, diagrams, and examples are retained.

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Linear Algebra

23 items

Determinants

3 items

Linear Algebra · Determinants

Lecture 1: Course Introduction

Postgraduate Entrance Exam Mathematics Study Notes: Lecture 1: Course Introduction. Original formulas, diagrams, and example problems are retained.

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Linear Algebra · Determinants

Lecture 2: Definition and properties of determinants

Postgraduate Entrance Exam Mathematics Study Notes: Lecture 2: Definition and Properties of Determinants. Retain original formulas, diagrams, and example problems.

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Linear Algebra · Determinants

Lecture 3: Calculation of Determinants

Postgraduate Entrance Exam Mathematics Study Notes: Lecture 3: Calculation of Determinants. Retain original formulas, diagrams, and example problems.

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Matrices

7 items

Linear Algebra · Matrices

Lecture 4: Definition of Matrices and Their Basic Operations

Postgraduate Entrance Exam Mathematics Study Notes: Lecture 4: Definition of Matrices and Their Basic Operations. Original formulas, diagrams, and example problems are retained.

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Linear Algebra · Matrices

Lecture 5: Inverse Matrices

Graduate Entrance Examination Mathematics study notes: Lecture 5: Inverse Matrices. Original formulas, diagrams, and examples are retained.

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Linear Algebra · Matrices

Lecture 6: Adjugate Matrices

Graduate Entrance Examination Mathematics study notes: Lecture 6: Adjugate Matrices. Original formulas, diagrams, and examples are retained.

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Linear Algebra · Matrices

Lecture 7: Elementary Transformations and Elementary Matrices

Postgraduate Entrance Exam Mathematics Study Notes: Lecture 7: Elementary Transformations and Elementary Matrices. Retain original formulas, diagrams, and example problems.

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Linear Algebra · Matrices

Lecture 8: Matrix Equations

Postgraduate Entrance Exam Mathematics Study Notes: Lecture 8: Matrix Equations. Retain original formulas, diagrams, and example problems.

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Linear Algebra · Matrices

Lecture 9: Equivalent Matrices

Postgraduate Entrance Exam Mathematics study notes: Lecture 9: Equivalent Matrices. Original formulas, diagrams, and examples are retained.

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Linear Algebra · Matrices

Lecture 10: Rank of a matrix

Postgraduate Entrance Exam Mathematics Study Notes: Lecture 10: Rank of Matrices. Retain original formulas, diagrams, and example problems.

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Vector Sets

4 items

Linear Algebra · Vector Sets

Lecture 11: Linear Dependence of Vectors and Vector Sets

Postgraduate Entrance Exam Mathematics study notes: Lecture 11: Linear Dependence of Vectors and Vector Sets. Original formulas, diagrams, and examples are retained.

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Linear Algebra · Vector Sets

Lecture 12: Maximal Linearly Independent Sets and Rank

Graduate Entrance Examination Mathematics study notes: Lecture 12: Maximal Linearly Independent Sets and Rank. Original formulas, diagrams, and examples are retained.

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Linear Algebra · Vector Sets

Lecture 13: Equivalent Sets of Vectors

Graduate Entrance Examination Mathematics study notes: Lecture 13: Equivalent Sets of Vectors. Original formulas, diagrams, and examples are retained.

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Linear Algebra · Vector Sets

Lecture 14: Vector Spaces

Postgraduate Entrance Exam Mathematics study notes: Lecture 14: Vector Spaces. Original formulas, diagrams, and examples are retained.

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Systems of Linear Equations

4 items

Linear Algebra · Systems of Linear Equations

Lecture 15: Homogeneous Systems of Linear Equations

Postgraduate Entrance Exam Mathematics study notes: Lecture 15: Homogeneous Systems of Linear Equations. Original formulas, diagrams, and examples are retained.

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Linear Algebra · Systems of Linear Equations

Lecture 16: Systems of Nonhomogeneous Linear Equations

Postgraduate Entrance Exam Mathematics Study Notes: Lecture 16: Systems of Nonhomogeneous Linear Equations. Original formulas, diagrams, and example problems are retained.

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Linear Algebra · Systems of Linear Equations

Lecture 17: Common Solutions of Two Systems of Equations

Postgraduate Entrance Exam Mathematics Study Notes: Lecture 17: Common Solutions to Two Systems of Equations. Retain original formulas, diagrams, and example problems.

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Linear Algebra · Systems of Linear Equations

Lecture 18: Equivalent Systems of Linear Equations

Graduate Entrance Examination Mathematics study notes: Lecture 18: Equivalent Systems of Linear Equations. Original formulas, diagrams, and examples are retained.

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Eigenvalues and Eigenvectors

2 items

Linear Algebra · Eigenvalues and Eigenvectors

Lecture 19: Eigenvalues and eigenvectors

Postgraduate Entrance Exam Mathematics Study Notes: Lecture 19: Eigenvalues and eigenvectors. Retain original formulas, diagrams, and example problems.

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Linear Algebra · Eigenvalues and Eigenvectors

Lecture 20: Similar Matrices

Graduate Entrance Examination Mathematics study notes: Lecture 20: Similar Matrices. Original formulas, diagrams, and examples are retained.

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Quadratic Forms

3 items

Linear Algebra · Quadratic Forms

Lecture 21: Definition and Matrix Representation of Quadratic Forms

Postgraduate Entrance Exam Mathematics study notes: Lecture 21: Definition and Matrix Representation of Quadratic Forms. Original formulas, diagrams, and examples are retained.

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Linear Algebra · Quadratic Forms

Lecture 22: Reducing Quadratic Forms to Standard and Canonical Forms

Graduate Entrance Examination Mathematics study notes: Lecture 22: Reducing Quadratic Forms to Standard and Canonical Forms. Original formulas, diagrams, and examples are retained.

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Linear Algebra · Quadratic Forms

Lecture 23: Positive-Definite Quadratic Forms

Graduate Entrance Examination Mathematics study notes: Lecture 23: Positive-Definite Quadratic Forms. Original formulas, diagrams, and examples are retained.

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Engineering Mathematics

1 items

Complex Numbers, Fourier Transforms, Probability and Linear Algebra

1 items

Engineering Mathematics · Complex Numbers, Fourier Transforms, Probability and Linear Algebra2026-07

Engineering Mathematics Map: Complex Numbers, Transforms and Probability

A dependency-based map of complex numbers, calculus, linear algebra, transforms and probability, with their uses in communications and signal processing.

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Learning note category

English

49 items

English Grammar

27 items

Topic Summaries

3 items

English Grammar · Topic Summaries

01 Simple Sentences — Summary

Graduate Entrance Examination English study notes: 01 Simple Sentences — Summary. Original examples, diagrams, and exercises are retained.

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English Grammar · Topic Summaries

02 Complex Sentences — Summary

Graduate Entrance Examination English study notes: 02 Complex Sentences — Summary. Original examples, diagrams, and exercises are retained.

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English Grammar · Topic Summaries

03 Complex-Sentence Analysis — Summary

Graduate Entrance Examination English study notes: 03 Complex-Sentence Analysis — Summary. Original examples, diagrams, and exercises are retained.

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Simple Sentences

10 items

English Grammar · Simple Sentences2024-02-28

Lecture 1: Grammar - Simple Sentences

Postgraduate English Study Notes: Lecture 1: Grammar - Simple Sentences. Original formulas, diagrams, and example questions are retained.

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English Grammar · Simple Sentences2024-02-29

Lecture 2: Tenses of Finite Verbs

Graduate Entrance Examination English study notes: Lecture 2: Tenses of Finite Verbs. Original examples, diagrams, and exercises are retained.

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English Grammar · Simple Sentences2024-03-03

Lecture 3: Modality and Voice of Finite Verbs

Graduate Entrance Examination English study notes: Lecture 3: Modality and Voice of Finite Verbs. Original examples, diagrams, and exercises are retained.

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English Grammar · Simple Sentences2024-03-04

Lecture 4: Passive voice

Postgraduate English Study Notes: Lecture 4: Passive Voice. Original formulas, diagrams, and example questions are retained.

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English Grammar · Simple Sentences2024-03-05

Lecture 5: Negation and Emphasis

Graduate Entrance Examination English study notes: Lecture 5: Negation and Emphasis. Original examples, diagrams, and exercises are retained.

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English Grammar · Simple Sentences2024-03-05

Lecture 6: Forms of Finite Verbs — Exam Strategies

Graduate Entrance Examination English study notes: Lecture 6: Forms of Finite Verbs — Exam Strategies. Original examples, diagrams, and exercises are retained.

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English Grammar · Simple Sentences2024-03-06

Lecture 7: Expanding Simple Sentences

Graduate Entrance Examination English study notes: Lecture 7: Expanding Simple Sentences. Original examples, diagrams, and exercises are retained.

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English Grammar · Simple Sentences2024-03-07

Lecture 8: Prepositional phrases

Postgraduate English Study Notes: Lecture 8: Prepositional phrases. Original formulas, diagrams, and example questions are retained.

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English Grammar · Simple Sentences2024-03-07

Lecture 9: Appositives and Parenthetical Expressions

Graduate Entrance Examination English study notes: Lecture 9: Appositives and Parenthetical Expressions. Original examples, diagrams, and exercises are retained.

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English Grammar · Simple Sentences2024-03-08

Lecture 10: Non-finite verbs

Postgraduate English Study Notes: Lecture 10: Non-finite verbs. Original formulas, diagrams, and example questions are retained.

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Complex Sentences

7 items

English Grammar · Complex Sentences2024-03-12

Lecture 11: Compound Sentences

Graduate Entrance Examination English study notes: Lecture 11: Compound Sentences. Original examples, diagrams, and exercises are retained.

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English Grammar · Complex Sentences2024-03-13

Lecture 12: Noun clauses

Postgraduate English Study Notes: Lecture 12: Noun Clauses. Original formulas, diagrams, and example questions are retained.

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English Grammar · Complex Sentences2024-03-18

Lecture 13: Relative Clauses

Graduate Entrance Examination English study notes: Lecture 13: Relative Clauses. Original examples, diagrams, and exercises are retained.

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English Grammar · Complex Sentences2024-03-18

Lecture 14: Adverbial clauses

Postgraduate English Study Notes: Lecture 14: Adverbial Clauses. Original formulas, diagrams, and example questions are retained.

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English Grammar · Complex Sentences2024-03-20

Lecture 15: The Subjunctive Mood

Graduate Entrance Examination English study notes: Lecture 15: The Subjunctive Mood. Original examples, diagrams, and exercises are retained.

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English Grammar · Complex Sentences2024-03-21

Lecture 16: Inverted sentences

Postgraduate English Study Notes: Lecture 16: Inverted Sentences. Original formulas, diagrams, and example questions are retained.

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English Grammar · Complex Sentences2024-03-24

Lecture 17: Emphatic Sentences

Graduate Entrance Examination English study notes: Lecture 17: Emphatic Sentences. Original examples, diagrams, and exercises are retained.

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Complex-Sentence Analysis

7 items

English Grammar · Complex-Sentence Analysis

Lecture 18: Parsing Complex Sentences with Punctuation

Graduate Entrance Examination English study notes: Lecture 18: Parsing Complex Sentences with Punctuation. Original examples, diagrams, and exercises are retained.

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English Grammar · Complex-Sentence Analysis

Lecture 19: Parsing Complex Sentences with Connectives

Graduate Entrance Examination English study notes: Lecture 19: Parsing Complex Sentences with Connectives. Original examples, diagrams, and exercises are retained.

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English Grammar · Complex-Sentence Analysis

Lecture 20: Parsing Complex Sentences by Identifying Subjects and Predicates

Graduate Entrance Examination English study notes: Lecture 20: Parsing Complex Sentences by Identifying Subjects and Predicates. Original examples, diagrams, and exercises are retained.

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English Grammar · Complex-Sentence Analysis2024-04-12

Lecture 21: Simplifying Complex Sentences

Graduate Entrance Examination English study notes: Lecture 21: Simplifying Complex Sentences. Original examples, diagrams, and exercises are retained.

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English Grammar · Complex-Sentence Analysis

Lecture 22: Split Structure

Graduate English Study Notes: Lecture 22: Split Structure. Retain original formulas, diagrams, and example questions.

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English Grammar · Complex-Sentence Analysis

Lecture 23: Nested structures

Graduate English Study Notes: Lecture 23: Nested Structure. Original formulas, diagrams, and example questions are retained.

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English Grammar · Complex-Sentence Analysis

Lecture 24: Parallel structures

Postgraduate English Study Notes: Lecture 24: Parallel Structure. Original formulas, diagrams, and example questions are retained.

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English Reading

7 items

Topic Summaries

1 items

English Reading · Topic Summaries

01 Reading Methodology — Summary

Graduate Entrance Examination English study notes: 01 Reading Methodology — Summary. Original examples, diagrams, and exercises are retained.

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Past Papers, 1996–2003

1 items

English Reading · Past Papers, 1996–2003

Lecture 1: Reading Methodology

Graduate Entrance Examination English study notes: Lecture 1: Reading Methodology. Original examples, diagrams, and exercises are retained.

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Past Papers, 2005–2009

5 items

English Reading · Past Papers, 2005–2009

Lecture 2: Reading Past Papers — 2005

Graduate Entrance Examination English study notes: Lecture 2: Reading Past Papers — 2005. Original examples, diagrams, and exercises are retained.

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English Reading · Past Papers, 2005–2009

Lecture 3: Reading Past Papers — 2006

Graduate Entrance Examination English study notes: Lecture 3: Reading Past Papers — 2006. Original examples, diagrams, and exercises are retained.

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English Reading · Past Papers, 2005–2009

Lecture 4: Reading Past Papers — 2007

Graduate Entrance Examination English study notes: Lecture 4: Reading Past Papers — 2007. Original examples, diagrams, and exercises are retained.

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English Reading · Past Papers, 2005–2009

Lecture 5: Reading Past Papers — 2008

Graduate Entrance Examination English study notes: Lecture 5: Reading Past Papers — 2008. Original examples, diagrams, and exercises are retained.

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English Reading · Past Papers, 2005–2009

Lecture 9: Reading Past Papers — 2009

Graduate Entrance Examination English study notes: Lecture 9: Reading Past Papers — 2009. Original examples, diagrams, and exercises are retained.

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English Writing

15 items

2011 Past Paper: Essay

1 items

English Writing · 2011 Past Paper: Essay

2011 Past Paper: Essay

Graduate Entrance Examination English study notes: 2011 Past Paper: Essay. Original examples, diagrams, and exercises are retained.

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2011 Past Paper: Practical Writing

1 items

English Writing · 2011 Past Paper: Practical Writing

2011 Past Paper: Practical Writing

Graduate Entrance Examination English study notes: 2011 Past Paper: Practical Writing. Original examples, diagrams, and exercises are retained.

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2012 Past Paper: Essay

1 items

English Writing · 2012 Past Paper: Essay

2012 Past Paper: Essay

Graduate Entrance Examination English study notes: 2012 Past Paper: Essay. Original examples, diagrams, and exercises are retained.

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2012 Past Paper: Practical Writing

1 items

English Writing · 2012 Past Paper: Practical Writing

2012 Past Paper: Practical Writing

Graduate Entrance Examination English study notes: 2012 Past Paper: Practical Writing. Original examples, diagrams, and exercises are retained.

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2017 Past Paper: Essay — Negative Trend

1 items

English Writing · 2017 Past Paper: Essay — Negative Trend

2017 Past Paper: Essay — Negative Trend

Graduate Entrance Examination English study notes: 2017 Past Paper: Essay — Negative Trend. Original examples, diagrams, and exercises are retained.

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2017 Past Paper: Practical Writing — Advice

1 items

English Writing · 2017 Past Paper: Practical Writing — Advice

2017 Past Paper: Practical Writing — Advice

Graduate Entrance Examination English study notes: 2017 Past Paper: Practical Writing — Advice. Original examples, diagrams, and exercises are retained.

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2018 Past Paper: Essay — Negative Trend

1 items

English Writing · 2018 Past Paper: Essay — Negative Trend

2018 Past Paper: Essay — Negative Trend

Graduate Entrance Examination English study notes: 2018 Past Paper: Essay — Negative Trend. Original examples, diagrams, and exercises are retained.

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2018 Past Paper: Practical Writing — Introduction

1 items

English Writing · 2018 Past Paper: Practical Writing — Introduction

2018 Past Paper: Practical Writing — Introduction

Graduate Entrance Examination English study notes: 2018 Past Paper: Practical Writing — Introduction. Original examples, diagrams, and exercises are retained.

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2021 Past Paper: Essay — Negative Trend

1 items

English Writing · 2021 Past Paper: Essay — Negative Trend

2021 Past Paper: Essay — Negative Trend

Graduate Entrance Examination English study notes: 2021 Past Paper: Essay — Negative Trend. Original examples, diagrams, and exercises are retained.

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2021 Past Paper: Practical Writing — Advice

1 items

English Writing · 2021 Past Paper: Practical Writing — Advice

2021 Past Paper: Practical Writing — Advice

Graduate Entrance Examination English study notes: 2021 Past Paper: Practical Writing — Advice. Original examples, diagrams, and exercises are retained.

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2022 Past Paper: Essay — Negative Trend

1 items

English Writing · 2022 Past Paper: Essay — Negative Trend

2022 Past Paper: Essay — Negative Trend

Graduate Entrance Examination English study notes: 2022 Past Paper: Essay — Negative Trend. Original examples, diagrams, and exercises are retained.

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2022 Past Paper: Practical Writing — Invitation

1 items

English Writing · 2022 Past Paper: Practical Writing — Invitation

2022 Past Paper: Practical Writing — Invitation

Graduate Entrance Examination English study notes: 2022 Past Paper: Practical Writing — Invitation. Original examples, diagrams, and exercises are retained.

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2023 Past Paper: Essay — Positive Trend

1 items

English Writing · 2023 Past Paper: Essay — Positive Trend

2023 Past Paper: Essay — Positive Trend

Graduate Entrance Examination English study notes: 2023 Past Paper: Essay — Positive Trend. Original examples, diagrams, and exercises are retained.

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2023 Past Paper: Practical Writing — Recruitment

1 items

English Writing · 2023 Past Paper: Practical Writing — Recruitment

2023 Past Paper: Practical Writing — Recruitment

Graduate Entrance Examination English study notes: 2023 Past Paper: Practical Writing — Recruitment. Original examples, diagrams, and exercises are retained.

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