Theorem은 Corollary, Lemma를 모두포함
Exercise는 새끼문제까지 모두 셌음







Walter Rudin - Principles of Mathematical Analysis
3rd edition



74ea8876b58568fe3be987e6429f2e2db8a2f2a07492eeec806f39cb




Ch1. The Real and Complex Number Systems

Definition 15개
Theorem 14개
Proposition 17개 (1장만 Proposition이 있음)
Exercise 31개

Ch2. Basic Topology

Definition 12개
Theorem 31개
Exercise 41개

Ch3. Numerical Sequences and Series

Definition 13개
Theorem 35개
Exercise 46개

Ch4. Continuity

Definition 10개
Theorem 21개
Exercise 30개

Ch5. Differentiation

Definition 3개
Theorem 12개
Exercise 47개

Ch6. The Riemann-StieltJes Integral

Definition 6개
Theorem 19개
Exercise 30개

Ch7. Sequences and Series of Functions

Definition 7개
Theorem 20개
Exercise 32개

Ch8. Some Special Functions

Definition 3개
Theorem 18개
Exercise 48개

Ch9. Functions of Several Variables

Definition 9개
Theorem 24개
Exercise 48개

Ch10. Integration of Differential Forms

Definition 7개
Theorem 20개
Exercise 51개

Ch11. The Lebesgue Theorh

Definition 15개
Theorem 29개
Exercise 18개



전체분량


Definition 97개
Theorem 142개
Exercise 276개









Friedberg - Linear Algebra 5th edition





79ec9d76e98b20aa5ae6fafb29f0070246718875893ca9bbd73a218ab1fbff635a6d64b3ce0075cd8e3631c45465a3b6






Ch1. Vector Spaces [Def 13, Thm 16, Exer 274]


1.1 Introduction [Def 0, Thm 0, Exer 16]

1.2 Vector Spaces [Def 1, Thm 2, Exer 45]

1.3 Subspaces [Def 2, Thm 2, Exer 52]

1.4 Linear Combinations and Systems of Linear Equations [Def 3, Thm 1, Exer 45]

1.5 Linear Dependence and Linear Independence
[Def 2, Thm 2, Exer 38]

1.6 Bases and Dimension [Def 2, Thm 6, Exer 66]

1.7 Maximal Linearly Independent Subsets
[Def 3, Thm 3, Exer 12]


Ch2. Linear Transformations and Matrices
[Def 24, Thm 42, Exer 341]


2.1 Linear Transformations, Null Spaces, and Ranges [Def 4, Thm 7, Exer 76]

2.2 The atrix Representation of a Linear Transformation [Def 6, Thm 1, Exer 37]

2.3 Composition of Linear Transformations
and Matrix Multiplication [Def 2, Thm 10, Exer 47]

2.4 lnvertibility and Isomorphisms
[Def 4, Thm 6, Exer 53]

2.5 The Change of Coordinate Matrix
[Def 0, Thm 4, Exer 32]

2.6 Dual Spaces [Def 2, Thm 5, Exer 47]

2.7 Homogeneous Linear Differential Equations with Constant Coefficients [Def 6, Thm 9, Exer 49]


Ch3. Elementary Matrix Operations and Systems of Linear Equations [Def 7, Thm 20, Exer 150]


3.1 Elementary Matrix Operations and Elementary Matrices [Def 2, Thm 2, Exer 22]

3.2 The Rank of a Matrix and Matrix Inverses
[Def 2, Thm 8, Exer 52]

3.3 Systems of Linear Equations-Theoretical Aspects [Def 1, Thm 5, Exer 39]

3.4 Systems of Linear Equations-Computational Aspects [Def 2, Thm 5, Exer 37]


Ch4. Determinants [Def 5, Thm 88, Exer 176]


4.1 Determinants of Order 2 [Def 1, Thm 2, Exer 28]

4.2 Determinants of Order n [Def 1, Thm 5, Exer 37]

4.3 Properties of Determinants [Def 1, Thm 3, Exer 52]

4.4 Summary- Important Facts about Determinants [Def 0, Thm 0, Exer 33]

4.5 A Characterization of the Determinant
[Def 2, Thm 3, Exer 26]


Ch5. Diagonalization [Def 17, Thm 30, Exer 257]


5.1 Eigenvalues and Eigenvectors
[Def 3, Thm 4, Exer 77]

5.2 Diagonalizability [Def 6, Thm 6, Exer 56]

5.3 Matrix Limits and Markov Chains
[Def 5, Thm 14, Exer 59]

5.4 Invariant Subspaces and the Cayley-Hamilton Theorem [Def 3, Thm 6, Exer 65]


Ch6. Inner Product Spaces [Def 36, Thm 72, Exer 523]


6.1 Inner Products and Norms [Def 5, Thm 2, Exer 74]

6.2 The Gram Schmidt Orthogonalization Process
and Orthogonal Complements [Def 3, Thm 9, Exer 53]

6.3 The Adjoint of a Linear Operator
[Def 2, Thm 10, Exer 50]

6.4 Normal and Self-Adjoint Operators
[Def 3, Thm 5, Exer 51]

6.5 Unitary and Orthogonal Operators and Their Matrices [Def 5, Thm 9, Exer 70]

6.6 Orthogonal Projections and the Spectral Theorem [Def 1, Thm 6, Exer 27]

6.7 The Singular Value Decomposition and the Pseudoinverse [Def 4, Thm 4, Exer 66]

6.8 Bilinear and Quadratic Forms
[Def 9, Thm 14, Exer 66]

6.9 Einstein's Special Theory of Relativity
[Def 0, Thm 5, Exer 11]

6.10 Conditioning and the Rayleigh Quotient
[Def 2, Thm 4, Exer 24]

6.11 The Geometry of Orthogonal Operators
[Def 2, Thm 4, Exer 31]


Ch7. Canonical Forms [Def 11, Thm 35, Exer 176]


7.1 The Jordan Canonical Form I
[Def 4, Thm 9, Exer 36]

7.2 The Jordan Canonical Form II
[Def 2, Thm 4, Exer 70]

7.3 The 1Iinimal Polynomial [Def 3, Thm 7, Exer 41]

7.4 The Rational Canonical Form 
[Def 2, Thm 15, Exer 29]


Appendices [Def 7, Thm 32]

A sets [X]
B functions [X]
C Fields [Def 1, Thm 3]
D Complex Numbers [Def 3, Thm 12]
E Polynomals [Def 3, Thm 17]



정리

Ch1. Vector Spaces [Def 13, Thm 16, Exer 274]

Ch2. Linear Transformations and Matrices
[Def 24, Thm 42, Exer 341]

Ch3. Elementary Matrix Operations and Systems of Linear Equations [Def 7, Thm 20, Exer 150]

Ch4. Determinants [Def 5, Thm 88, Exer 176]

Ch5. Diagonalization [Def 17, Thm 30, Exer 257]

Ch6. Inner Product Spaces [Def 36, Thm 72, Exer 523]

Ch7. Canonical Forms [Def 11, Thm 35, Exer 176]

Appendices [Def 7, Thm 32]



전체 분량 [Def 120 Thm 335 Exer 1897]

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