Elective course 3-5: For convex polyhedron, there must be a formula: V+F-E=2, where V is the number of vertices of polyhedron P, F is the number of faces of polyhedron P, E is the number of edges of polyhedron P, and X(P) is the Euler characteristic of polyhedron P. If P can be homeomorphic on a sphere (in a popular sense, it can be expanded and stretched on a sphere), then X(P)=2. This is related to topology. Let me tell you about topology first. Let me tell you this formula again.
Elective 3-6: I think junior high school is engaged in the equal division of rulers and rulers. The full Greeks came up with several more questions: the angle is divided into three parts, the angle is divided into two parts, and the equal area is rounded into a square, so you can use a ruler. Today, when most people have something to do, people look at other problems (1895, the great mathematician Klein proved that these three problems have no solutions). Then why can't you find a solution by citing N theorems when you are studying the first line? Let's talk about the number field first. Let f be a number ring. If a, b∈F and a≠0 are arbitrary, then b/a ∈ f; F is called the number field. For example, rational number set, real number set and complex number set are all number fields. Number ring: Let s be a nonempty subset of a complex set. If the sum, difference and product of any two numbers in S still belong to S, then S is called a number ring. For example, integer set Z is a number ring, rational number set Q, real number set R and complex number set C are all number rings. ) Now we have to leave, get rid of QRC and enter the new world.
Elective 4-3: Sequences are also functions, which is undeniable. Only its domain is a positive integer. Whether we talk about derivative, integral, differential or limit to learn derivative, we all have a premise: "Unless otherwise specified, the functions involved in this question are all continuous functions." It's very clear. Continuity must be derivable, derivable and continuous, which is an important conclusion of differential calculus of unary functions. We know that derivatives are defined by limits. What about functions such as series (discrete functions)?
Definition: Δ f (x) = [f (x+1)-f (x)] is the first-order difference of a discrete function, similar to the derivative, and there may be higher-order differences. An equation with an unknown function difference is called a difference equation. The equation also has a specific solution. Meanwhile, if there is a difference, there will be a deficit. δ here, difference operator, has his unique properties.
Elective 4-8: Overall planning is a science. Although the national departments have many functions, they all have to make overall plans in essence, and there are specialized disciplines to make overall plans for research. The basic model in the master planning method is the master planning diagram (network diagram). Without a plan, it will be intuitive. It uses nodes, arrows and corresponding numbers to describe the relationship between the whole and its parts, between its parts and between them and the outside world. Starting from the basic model, we need to choose other models suitable for it according to different overall goals.
It is natural that graph theory problems arise from this (look at the pictures and talk). The earliest example of graph theory is probably the seven-bridge problem. Then there is the problem of four-color map. It can get rid of overall planning and do some applications by itself.
Elective course 4- 10: Physics 3- 1 has a section on logic circuits.
What is Boolean algebra? A Boolean algebra (also called logical algebra) refers to an ordered quadruple < b, ∨, ∧, * >, where b is a non-empty set, ∨ and ∧ are two binary operations defined on b, and * is a unary operation defined on b, and they can form a Boolean if they meet certain conditions. Say two nouns: and logic, or logic, and then you will think of something (if you are a science student). Don't go too deep, this is what we use. We can remove the switch, as long as there is a logical operation, we can calculate the cost.
Elective course 4-9 is not available in Northeast China (because you don't study), so you can only buy it at Taobao store in Beijing (or South China). The books mentioned just now have not been examined by the primary and secondary school textbook review Committee, so naturally there are no books. The latest is elective course 3-3(2065 438+0 1 first review).