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資格考考試範圍
代數通論
Algebra (by Hungerford)
(i) Groups
(ii) The structure of groups
(iii) Rings
(iv) Modules
(v) Fields and Galois Theory
(vi) The structure of fields
(vii) Linear Algebra
(viii) Commutative Rings and Modules
(ix) The structure of rings
分析通論
Real and Complex Analysis (3rd ed.) (by Walter Rudin) Ch.1~9.
Real Analysis (3rd ed.) (by H.L.Royden) Ch.3~6,10~13.
(i) Measure spaces and measurable functions
(ii) Lebesgue measure
(iii) Abstract Lebesgue integration
(iv)
Lp -spaces
(v) Fundamentals of functional analysis on Hilbert spaces and Banach spaces
(vi) Differentiation and Radon-Nikodym theorem
(vii) Product measures and Fubini theorem
(viii) Borel measures
泛函分析
A course in Functional Analysis (by John B. Conway)
(i) Hillbert spaces
(ii) Operators on Hilbert spaces
(iii) Banach spaces
(iv) Locally convex spaces
(v) Weak topologies
(vi) Linear operator on a Banach space
(vii) Banach algebras and spectral theory for operators on a Banach space
常微分方程
Differential Equations, Dynamical Systems, and Linear Algebra (by Hirsch and Smale)
(i) First examples
(ii) Newton’s equation and Kepler’s law
(iii) Linear systems with constant coefficients and real eigenvalues
(iv) Linear systems with constant coefficients and complex eigenvalues
(v) Linear systems and exponential of operators
(vi) Linear systems and canonical forms of operators
(vii) Contractions and generic properties of operators
圖論與組合理論
Applied Combinatorics (by Alan Tucker)
Introduction to Graph theory (by Gary Chartrand & Ping Zhang)
Introduction to Graph theory (by Douglas B. West)
(i) Generating functions
(ii) Recurrence relations
(iii) Pigeonhole Principle
(iv) Inclusion-exclusion formula
(v) Degrees
(vi) Isomorphic graphs
(vii) Trees
(viii) Eulerian graphs and Hamilton graphs
(ix) Ramsey numbers
(x) Matching
(xi) Connectivity of graphs
(xii) Planar graphs
(xiii) Coloring
機率論
A Course in Probability Theory (by Kai Lai Chung)
Probability and Measure (Billingsley)
Probability with martingales(by David Williams)
(i) classes of sets, measure and probability spaces
(ii) random variable, expectation, independence and distributions
(iii) Integration and Expectation
(iv) convergence concepts
(v) Uniform Integrability
(vi) characteristic function and The Central Limit Theorem
(vi) conditional expectation, conditional independence, martingales
迴歸與變異數分析
Linear Models in Statistics (by A.C. Rencher and G.B. Schaalje 2008)
Linear Regressive Analysis (by Seber)
Design Analysis of Experiments (by D.C. Montgomery)
(i) Estimation
(ii) Tests of Hypotheses and Contidence Intervals
(iii) Model Validation and Diagnostics
(iv) Analysis of Variance Model
(v) Linear Mixed Models
(vi) Block Design, Incomplete Block Design
(vii) Factorial Design, Fractional, Factorial Design
(viii) Nested and Split-plot Design
數理統計
1.Statistical Inference(2nd Edition) G. Casella and R.L. Berger
2.Mathematical Statistics, Basic ideas and selected topics, Vol.1(2nd Edition) P.J. Bickel
and K.A. Doksum
3.Introduction to probability and Mathematical Statistics (by V.K. Rohatgi)
(i) Distributions
(ii) Multiple random variables and their properties
(iii)Theory of point estimation
(iv) Hypothesis testing
(v) Interval estimators
(vi) Asymptotic approximation
演算法
Introduction to Algorithms, Second Edition (by Thomas H. Cormen, Charles E. Leiserson,
Ronald L. Rivest and Clifford Stein)
Introduction to Algorithms (by U. Manber)
Introduction to the Design and Analysis of Algorithms (by R. C. T. Lee, S . S. Tseng, R. C.
Chang and Y. T. Tsai)
(i) Analysis of Algorithms
(ii) Sorting
(iii) Data Structure
(iv) Dynamic Programming
(v) Greedy Algorithms
(vi) Amortized Analysis
(vii) Data Structures for Disjoint Sets
(viii) Graph Algorithms
(ix) NP-completeness
作業系統
Operating System Concepts (by Abraham Silberschatz, Peter Baer Galvin, Greg Gagne)
Distributed systems - Principles and Paradigms (by Andrew S. Tanenbaum, Maarten van
Steen)
(i) System Structures
(ii) Process Concept
(ii) Communication
(iv) Threaded Programming
(v) Process Scheduling
(vi) Synchronization
(vii) Deadlocks
(viii) Memory-Management Strategies
(ix) Virtual-Memory Management
(x) File System
(xi) Fault Tolerance
程式語言
Introduction to Automata Theory, Languages and Computation (by Hopcroft, Motwani &
Ullman)
Introduction to Languages and Theory of Computation (by J. Martin)
Introduction to Theory of Computation (by Sipser)
(i) Finite automata and regular languages
Deterministic/Nondeterministic finite automata
Regular languages and regular grammars
Properties of regular languages
(ii) Context-free grammars and languages
Context-free grammars
Pushdown automata
Properties of context-free languages
(iii) Turing machine and decidability
(iv) Computational complexity
資料庫系統
Fundamentals of Database Systems (by Ramakrishnan & Gehrke)
Database System: The Complete Book (by Garcia-Molina, Ullman & Widom)
Database System Concepts (by Silberschatz, Korth & Sudarsan)
(i) Data models and relational model
Relational data model
Relational algebra
Relational query languages (SQL)
(ii) Data storage and indexing
Secondary storage management
Index structures
(iii) Database design theory and methodology
Functional dependencies and normalization for relational databases
Relational database design algorithms
(iv) Query processing and optimization
(v) Transaction management
Transaction processing
Concurrency control
Recovery techniques
(vi) Parallel and distributed database
(vii) Object-oriented database