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Computer Mathematics 2019 / Lecture 10, Part 1: The Chinese Remainder Algorithm

easyarithmetican / atelier aterui
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The Chinese Remainder Algorithm (in Japanese). Note that question answering session has been closed. Please leave your questions or comments on YouTube page. Course information (in Japanese): https://www.math.tsukuba.ac.jp/~terui... Akira Terui. College of Mathematics, University of Tsukuba, Tsukuba, Japan. ...more
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Computer Mathematics 2019 / Lecture 10, Part 1: The Chinese Remainder Algorithm
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119Views
2019Jun 25
The Chinese Remainder Algorithm (in Japanese). Note that question answering session has been closed. Please leave your questions or comments on YouTube page. Course information (in Japanese): https://www.math.tsukuba.ac.jp/~terui... Akira Terui. College of Mathematics, University of Tsukuba, Tsukuba, Japan.

Follow along using the transcript.

easyarithmetican / atelier aterui

7.3K subscribers

計算機数学I (2019)
1

Computer Mathematics 2019 / Lecture 1, Part 1: Components of a computer system

easyarithmetican / atelier aterui
2

Computer Mathematics 2019 / Lecture 1, Part 2: Inside of a computer

easyarithmetican / atelier aterui
3

Computer Mathematics 2019 / Lecture 1, Part 3: Computer memory

easyarithmetican / atelier aterui
4

Computer Mathematics 2019 / Lecture 2, Part 1: Expression of integers and two's complement

easyarithmetican / atelier aterui
5

Computer Mathematics I (2019) / Lecture 2, Part 2: Floating-point numbers

easyarithmetican / atelier aterui
6

Computer Mathematics I (2019) / Lecture 2, Part 3: Rounding error and machine epsilon

easyarithmetican / atelier aterui
7

Computer Mathematics 2019 / Lecture 3, Part 1: Expression of multi-precision integers

easyarithmetican / atelier aterui
8

Computer Mathematics 2019 / Lecture 3, Part 2: Addition of multiple-precision integers

easyarithmetican / atelier aterui
9

Computer Mathematics 2019 / Lecture 3, Part 3: Expression of algorithm

easyarithmetican / atelier aterui
10

Computer Mathematics 2019 / Lecture 3, Part 4: Algorithm for addition of multiple-precision integers

easyarithmetican / atelier aterui
11

Computer Mathematics 2019 / Lecture 4, Part 1: Computational complexity and asymptotic notation

easyarithmetican / atelier aterui
12

Computer Mathematics 2019 / Lecture 4, Part 2: Complexity of addition of multi-precision integers

easyarithmetican / atelier aterui
13

Computer Mathematics 2019 / Lecture 4, Part 3: Addition of univariate polynomials

easyarithmetican / atelier aterui
14

Computer Mathematics 2019 / Lecture 5, Part 1: The Horner's rule

easyarithmetican / atelier aterui
15

Computer Mathematics 2019 / Lecture 5, Part 2: Binary-Decimal conversion of nonnegative integers

easyarithmetican / atelier aterui
16

Computer Mathematics 2019 / Lecture 5, Part 3: Binary-Decimal conversion of decimals

easyarithmetican / atelier aterui
17

Computer Mathematics 2019 / Lecture 5, Part 4: Binary-Decimal conversion: an example

easyarithmetican / atelier aterui
18

Computer Mathematics 2019 / Lecture 6, Part 1: Multiplication of univariate polynomials

easyarithmetican / atelier aterui
19

Computer Mathematics 2019 / Lecture 6, Part 2: Multiplication of multi-precision integers

easyarithmetican / atelier aterui
20

Computer Mathematics 2019 / Lecture 6, Part 3: Division with remainder

easyarithmetican / atelier aterui
21

Computer Mathematics 2019 / Lecture 7, Part 1: Euclidean domain

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22

Computer Mathematics 2019 / Lecture 7, Part 2: The Euclidean algorithm

easyarithmetican / atelier aterui
23

Computer Mathematics 2019 / Lecture 7, Part 3: The Extended Euclidean algorithm

easyarithmetican / atelier aterui
24

Computer Mathematics 2019 / Lecture 8, Part 1: Property of the Extended Euclidean algorithm

easyarithmetican / atelier aterui
25

Computer Mathematics 2019 / Lecture 8, Part 2: Calculating modular inverse

easyarithmetican / atelier aterui
26

Computer Mathematics 2019 / Lecture 9, Part 1: Property of the Extended Euclidean algorithm (2)

easyarithmetican / atelier aterui
27

Computer Mathematics 2019 / Lecture 9, Part 2: Continued fraction expansions of rational numbers

easyarithmetican / atelier aterui
28

Computer Mathematics 2019 / Lecture 9, Part 3: Continued fraction approximation

easyarithmetican / atelier aterui
▶

Computer Mathematics 2019 / Lecture 10, Part 1: The Chinese Remainder Algorithm

easyarithmetican / atelier aterui
30

Computer Mathematics 2019 / Lecture 10, Part 2: The Chinese Remainder Algorithm: an example

easyarithmetican / atelier aterui
31

Computer Mathematics 2019 / Lecture 11, Part 1: Rational reconstruction

easyarithmetican / atelier aterui
32

Computer Mathematics 2019 / Lecture 11, Part 2: Recovering fractions from the decimal expansions

easyarithmetican / atelier aterui
33

Computer Mathematics 2019 / Lecture 12, Part 1: Time complexity of matrix multiplications

easyarithmetican / atelier aterui
34

Computer Mathematics 2019 / Lecture 12, Part 2: Matrix multiplications with Modular algorithm

easyarithmetican / atelier aterui
35

Computer Mathematics 2019 / Lecture 12, Part 3: Time complexity of modular matrix multiplications

easyarithmetican / atelier aterui
36

Computer Mathematics 2019 / Lecture 13, Part 1: Time complexity for division of polynomials

easyarithmetican / atelier aterui
37

Computer Mathematics 2019 / Lecture 13, Part 2: Time complexity for division of integers

easyarithmetican / atelier aterui
38

Computer Mathematics 2019 / Lecture 13, Part 3: Time complexity for the Chinese Remainder Algorithm

easyarithmetican / atelier aterui
39

Computer Mathematics 2019 / Lecture 14, Part 1: Karatsuba's multiplication algorithm for integers

easyarithmetican / atelier aterui
40

Computer Mathematics 2019 / Lecture 14, Part 2: Time complexity of Karatsuba's algorithm

easyarithmetican / atelier aterui
41

Computer Mathematics 2019 / Lecture 14, Part 3: Karatsuba's algorithm for univariate polynomials

easyarithmetican / atelier aterui
42

Computer Mathematics 2019 / Lecture 15, Part 1: Evaluation and interpolation of polynomials

easyarithmetican / atelier aterui
43

Computer Mathematics 2019 / Lecture 15, Part 2: Fast Fourier Transformation (FFT) Algorithm

easyarithmetican / atelier aterui
44

Computer Mathematics 2019 / Lecture 15, Part 3: Examples and time complexity of the FFT algorithm

easyarithmetican / atelier aterui
45

Computer Mathematics 2019 / Lecture 15, Part 5: Fast multiplication of polynomials using the FFT

easyarithmetican / atelier aterui