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Problem Drill Session
Multiple Choice
Long Question
Mixed Practice
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CUHK Maths Question Bank
Problem Drill Session
Multiple Choice
Long Question
Mixed Practice
Number of Questions:
Select Topics (Optional):
Group Theory
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Basic Group Concepts and Lagrange’s Theorem
Normal Subgroups and Quotient Groups
Group Homomorphisms and Isomorphisms
Series of Groups (Composition / Derived)
Isomorphism Theorems for Groups
Structure of Finitely Generated Abelian Groups
Free Groups, Generating Sets, Presentations
Group Actions and Cayley’s Theorem
Sylow Theorems and p-subgroups
Ring Theory
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Definitions, Examples and Basic Properties of Rings
Ring Homomorphisms and Isomorphisms
Ideals: Prime and Maximal
Factor Rings / Quotient Rings
Integral Domains, Fields, Ring of Fractions
Unique Factorization Domains (UFDs)
Principal Ideal Domains (PIDs)
Structure Theorem for Finitely Generated Modules over PIDs
Linear Algebra & Vector Spaces
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Vector Space
Subspace
Span, Linearly (in-)dependent
Basis, (In-)finite-dimensional, Dimension
Linear Transformations & Structure
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Linear Transformations
Null space, Range, Dimension Theorem
Matrix Representation of a Linear Transformation
Invertibility, Isomorphism
Change of Coordinates
Eigen-Theory & Advanced Linear Algebra
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Eigenvalue, Eigenvector, Diagonalizable Linear Transformation
Diagonalizability
Invariant Subspace, Cayley-Hamilton Theorem
Inner Product Spaces & Operator Theory
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Inner Product Space
Gram-Schmidt Orthogonalization
Orthogonal Complement
Adjoint of a Linear Operator
Characterisation of Normal and Self-Adjoint Operators
Unitary/Orthogonal Operators
Spectral Decomposition
Parameter Estimation
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Unbiased Estimation
Maximum Likelihood Estimation
Method of Moments
Confidence intervals
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Confidence Interval for Difference of Two Means
Confidence Interval for Proportions
Confidence Interval for Means
Hypothesis testing
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Power
Tests about Means
Critical Region and p-values
Nonparametric
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Order Statistics
Nonparametric Confidence Intervals
Nonparametric Hypothesis Tests
ANOVA
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Two-way ANOVA
One-way ANOVA
Linear regression
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Linear Regression
Likelihood ratio tests
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Likelihood Ratio Tests
ARMA models
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Stationarity
Parameter Computation
ACF and PACF
Forecasting
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Forecasting
Parameter Estimation in Time Series
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Parameter Estimation - MLE approaches
Parameter Estimation - Other approaches
GARCH
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GARCH
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