Foreword:
Although the teacher announced the question types during the online get out of class, he did not say the specific difficulty and depth.
After the exam this afternoon, I felt that the short-answer questions and calculation questions were still quite difficult, so I typed out today's questions while I still have memory, and gave a reference to the difficulty of friends who choose courses later.
The original question should not be reissued, but the general difficulty and depth of the question should be shown to the students who choose courses later through the question.
10 multiple choice questions + 10 multiple choice questions + 5 true or false questions:
It's not too difficult, it's all the questions in the back of the online video. Before the exam, brush them up, add the knowledge points notes I sent before, and review them together. It's not difficult to get a score of more than 90%.
The pitfalls I encountered in this exam: number system (forgetting that real numbers are seamless on the number axis), Riemann's conjecture
4 short answer questions, 5 points each ( not the original question , just express it in your own language based on memory):
1. Please briefly describe how to use the RSA encoding method to encrypt and decrypt files through the N and n given by the other party;
RSA encoding method: the difficulty of factorizing extremely large integers determines the reliability of the RSA algorithm
（1）p、q→N=p*q
(2) The smaller number n makes n and (p-1) and (q-1) mutually prime
(3) m→mn-1 is a multiple of (p-1)(q-1)→mn = k(p-1)(q-1)+1
Publicly available: N, n
Encrypted transmission process (Euler's theorem):
(1) The remainder obtained from plaintext x → x to the nth power/N → ciphertext y
(2) The remainder obtained from ciphertext y → y to the m power/N → plaintext x
Example: p = 3 q = 11 p - 1 = 2 q - 1 = 10
A. N = 33, choose n = 7 → public key
B、mn - 1 = 7m - 1
= k*2*10 = 20k
→m = (20k + 1) / 7
C. Take k = 1, then m = 3
2. What is the most fundamental difference between non-Euclidean geometry and Euclidean geometry? The relationship between non-Euclidean geometry and relativity?
Non-Euclidean Geometry (Lobachevsky Geometry + Riemannian Geometry): Overturning the Fifth Postulate
3. A point on a plane can be regarded as a vector or as a complex number. What is the significance of the two?
4. Briefly describe the content of Fermat's theorem, and whether Fermat's theorem has been proved?
Fermat's conjecture: When the integer n>2, there is no positive integer solution for x^n+y^n=z^n.
The proof of Fermat's conjecture was completed by British mathematician Andrew Wiles in 1994
4 calculation questions, 7 points for the first two questions, and 8 points for the last two questions ( not the original question , just express it in your own language according to memory):
1. Please use the 25 numbers 3, 7, 11, ..., 95, 99 (4n+3 arithmetic sequence) to construct a magic square of order 5 and calculate the magic sum (I thought it would not be so difficult, completely No preparation, this question is empty)
2. Can the following four figures be drawn in one stroke? If yes, draw the starting point, end point and direction. If not, explain the reason
Graphics don’t matter, anyway, the number of singular points that can be drawn with one stroke is at most 0 or 2, count how many lines are connected to each point, and see how many singular points there are
3. The five cards are 5 of diamonds, 7 of spades, K of diamonds, 2 of hearts, and Q of clubs. Which card should he give to Party A? How to lay out the remaining four cards? Why do you want to pose like this? (It’s actually poker magic, it’s very simple)
→ The first card is the same suit and the difference is not more than six → Give the square 5
→The remaining three cards are placed out of five → medium and large → Q 2 7
4. There are 2022 smurfs and 2023 red elves. If you touch the same color, you will become a smurf. If you collide with different colors, you will become a red elf. In the end, there will be only one elf left.
(1) How many times did the sprites collide?
(2) What color is the last elf? Why?