1.首先问你听不听得清楚：一定要说不太清楚，为自己留有余地呀。
2.Are you ready？ 就开始了
3.calculus： differentiate x^cosx, integrate x^3*logx(积X^n注意别积错)=X^4/4*logx-x^4/16+C
4.Fourier expansion, what’s the centre point (0) of x*cosx
5.Probability: pdf of exponential distribution, a question, explain the memorylessness of exponential distribution (唯一的一句”cool!”)
6.Linear Algebra: eigenvalue, eigenvector, how many eigenvalues and eigenvectors do a n*n vector has?
What’s the relation between the trace(矩阵的迹) of A and lamda?
As sum of the elements on the main diagonal , the trace of a matrix is the sum of the (complex) eigenvalues.The characteristic polynomial of a matrix can be written in terms of the trace and determinant, eg. Det
=det[A-λI2]= λ2-λtr(A)+det(A)
7.C++ (notice! It’s different from C!)what’s the difference between a class and structure?
As a value type, each structure variable is permanently bound to an individual structure instance.However, classes are reference types, and an object variable can refer to various class instances.This difference affects the usage of them in ways: eg. When you assign one structure variable to another, or pass a structure instance to a procedure argument, the current values of all the variable members are copied to the new structure. When you assign one object variable to another, or pass an object variable to a procedure, only the reference pointer is copied.
In object-oriented programming, a class is a construct that is used as a blueprint to create instances of itself – referred to as class instances, class objects, instance objects or simply objects.
Structures and classes differ in the following particulars:
- Structures are value types; classes are reference types.
- Structures use stack allocation; classes use heap allocation.
- All structure members are Public by default; class variables and constants are Private by default, while other class members are Public by default. This behavior for class members provides compatibility with the Visual Basic 6.0 system of defaults.
- A structure must have at least one nonshared variable or event member; a class can be completely empty.
- Structure members cannot be declared as Protected; class members can.
- A structure procedure can handle events only if it is a Shared Sub procedure, and only by means of the AddHandler statement; any class procedure can handle events, using either the Handles keyword or the AddHandler statement.
- Structure variable declarations cannot specify initializers, the New keyword, or initial sizes for arrays; class variable declarations can.
- Structures implicitly inherit from the ValueType class and cannot inherit from any other type; classes can inherit from any class or classes other than ValueType.
- Structures are not inheritable; classes are.
- Structures are never terminated, so the common language runtime (CLR) never calls the Finalize method on any structure; classes are terminated by the garbage collector, which calls Finalize on a class when it detects there are no active references remaining.
- A structure does not require a constructor; a class does.
- Structures can have nonshared constructors only if they take parameters; classes can have them with or without parameters.
Because structures are value types, each structure variable is permanently bound to an individual structure instance. But classes are reference types, and an object variable can refer to various class instances
This distinction affects your usage of structures and classes in the following ways:
- A structure variable implicitly includes an initialization of the members using the structure's parameterless constructor. Therefore, Dim S As Struct1 is equivalent to Dim S As Struct1 = New Struct1().
When you assign one structure variable to another, or pass a structure instance to a procedure argument, the current values of all the variable members are copied to the new structure. When you assign one object variable to another, or pass an object variable to a procedure, only the reference pointer is copied.
- You can assign the value Nothing to a structure variable, but the instance continues to be associated with the variable. You can still call its methods and access its data members, although variable members are reinitialized by the assignment. In contrast, if you set an object variable to Nothing, you dissociate it from any class instance, and you cannot access any members through the variable until you assign another instance to it.
- An object variable can have different class instances assigned to it at different times, and several object variables can refer to the same class instance at the same time. Changes you make to the values of class members affect those members when accessed through another variable pointing to the same instance. Structure members, however, are isolated within their own instance. Changes to their values are not reflected in any other structure variables, even in other instances of the same Structure declaration.
- Equality testing of two structures must be performed with a member-by-member test. Two object variables can be compared using the Equals method. Equals indicates whether the two variables point to the same instance.
8.Finance: what’s intrinsic value/ time value?
Of the three options (in the money, at the money, out of the money), which has the largest time value?
From B-S model, get some intuition
Out of the money options trade for a much smaller dollar amount, but they are 100% time premium. As the stock approaches the strike price, the dollar value of the stock option goes up. At the money stock options are also 100% time premium. Once the stock option goes in the money, it starts picking up intrinsic value on a percentage basis and on a dollar basis. Hence, the time value component decreases.
out of the money options can trade at much higher implied volatilities. If you believe the stock is going to make a significant move, buying at the money options can be an effective option trading strategy. Time value is also called time premium
9.any question?
祝大家好运！也为自己的终面攒人品~
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