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https://minireference.com/static/tutorials/linear_algebra_in_4_pages.pdf

https://dacon.io/forum/407751?page=1&dtype=recent&fType=&category=forum 딥러닝에 유용한 40개 + 13개수학 기호 dacon.ioChatGPT 가 열일 하네요. 자주 사용되는 수학기호 40개 +   Some Common Mathematical Symbols and Abbreviations 에서 13개 추가 했습니다.13개 출처 : Some Common Mathematical Symbols and Abbreviations (with History) Isaiah Lankham, Bruno Nachtergaele, Anne Schilling (January 21, 2007)논문 보다가 가끔 생각나지 않을때Here are the top 40 mathema..

Inclusion-Exclusion Formula Question 1 It is known that two events A and B in some probability space have probabilities 0.7 and 0.8. What is the minimal possible probability of an event "A and B" (the intersection of both events)? 0.7 + 0.8 - 1 = 0.5 Recall the inclusion and exclusion formula: Pr[A or B] = Pr[A] + Pr[B] - Pr[A and B]. This probability could not exceed 1, and Pr[A] + Pr[B] = 1.5,..

Q: What is the fraction of beans that end near the center (bins 40-60 among 0-100) for the ideal Galton board with 100 layers? (You may try to write a program, or use some scientific computations tool. For such a problem wolfram alpha should be enough.) A: The fraction of beans that end near the center (bins 40-60 among 0-100) for an ideal Galton board with 100 layers can be calculated using the..

Definition. We say that two numbers a and b are congruent modulo m if they have the same remainder when divided by m. We denote this by a ≡ b mod m We say integers a and b are "congruent modulo n" if their difference is a multiple of n. For example, 17 and 5 are congruent modulo 3 because 17 - 5 = 12 = 4⋅3. It can be expressed by 17 ≡ 5 mod 3. https://aimath.org/news/congruentnumbers/modulo.html..

a, b = 15, 4 print(a // b, a % b) print(divmod(a, b)) result) 3 3 (3, 3) The divmod(a, b) function is a built-in function in Python that takes two numbers as arguments and returns a tuple containing two values: the quotient (the result of the floor division a // b) and the remainder (a % b). Essentially, it combines the operations of floor division and modulo in a single function.

Question) There is a pile of 11 rocks. Two players take rocks from the pile in turns. In each turn a player can either take one or two rocks from the pile. The player that takes the last rock wins the game. You move first. Answer) You need to play in such a way that you maintain the strategy of leaving a multiple of 3 for the opponent. ex) You Take two rocks Your opponent Take two rocks You Take..

The table below gives a summary of the four selection schemes. Question) We have an unlimited supply of tomatoes, bell peppers and lettuce. We want to make a salad out of 4 units among these three ingredients (we do not have to use all ingredients). The order in which we use the ingredients does not matter. How many different salads we can make? Answer) To solve this problem, we can use the conc..

from itertools import product for t in product('abc', repeat=2): print(*t, sep='', end=' ') Result) aa ab ac ba bb bc ca cb cc This usage of the asterisk (`*`) is known as the unpacking operator in Python. It is used to unpack the elements of the iterable `t`. Here's a breakdown of what's happening: - `product('abc', repeat=2)` generates the Cartesian product of the string `'abc'` with itself, r..

In Python, when working with sets: The union operation is performed using the | operator. The union of two sets is a set containing all the elements that are in either of the two sets. For example, if set1 = {1, 2, 3} and set2 = {3, 4, 5}, then set1 | set2 would result in {1, 2, 3, 4, 5}. The intersection operation is performed using the & operator. The intersection of two sets is a set containi..

Summary. Invariants are important tools for proving impossibility, termination, and various bounds. Invariants may take many forms: numbers, "parity", equations, inequalities. To prove impossibility, one finds a quantity that never changes during a process. To prove that a process terminates in a number of steps, one usually finds a quantity that decreases at every step. Double counting is a met..

Q) There are two equally sized cups: cup 1 contains coffee and cup 2 contains milk. Both cups are half full (we are optimists). Your favorite drink is 1/3 coffee and 2/3 milk. Can you get such a drink in cup 1 by transferring (any amount of) liquid between the two cups? Any amount of your favorite drink would work --- the right proportion is what matters. A) It's impossible to create a drink wit..

Q) In a group of 27 students every girl knows four boys and every boy knows five girls. Find the number of boys in the group. A) To solve this problem, let's denote the number of boys in the group as B and the number of girls as G. We know that the total number of students in the group is 27, so we can express the relationship between the number of boys and girls as: G+B=27 We also know that eac..

"Recursion" is a way of defining some mathematical object (including a function or computation whose definition involves a recursive algorithm); "Induction" is a way of proving some mathematical statement. Extremely often, if a mathematical statement is made about a recursively-defined object, then the proof of that statement will involve induction. https://math.stackexchange.com/questions/37792..

Problem) There are n individuals at a party, and some of them have shaken hands. Prove that there are two individuals who have participated in the same number of handshakes. Solution) To prove that there are two individuals who have participated in the same number of handshakes at a party with n individuals, we can use the pigeonhole principle. First, let's consider the possible number of handsh..