Math & Computer Science

Question 1

What is dependency injection?

Answer 1

Rather than a client object creating its own dependencies or services, they are supplied by someone else so that the client doesn’t need to know how to create the service

Question 2

What are eigenvectors and eigenvalues?

Answer 2

Eigenvectors of a linear transformation (matrix) are not changed except in magnitude (the corresponding eigenvalue). They can form the basis vectors of a transformation

Question 3

What is a multiplexer?

Answer 3

A logic gate that toggles between the value of 2 inputs depending on the selector

Question 4

What does an ALU do? How is it made?

Answer 4

It can do many different calculations (AND, NOT, addition, negation, etc) on inputs depending on several other inputs that can be relatively elegantly designed

Question 5

How can you create memory from NAND gates?

Answer 5

Build a flip-flop using a looped NAND gate

Question 6

What is machine language?

Answer 6

Binary instructions to a computer corresponding to different ALU calculations and storage into registers and memory

Question 7

What is assembly?

Answer 7

A human readable version of machine language e.g. D=A+1, @variable with labels

Question 8

What are the 3 main components of a computer?

Answer 8

ROM (instructions), CPU, and Memory

Question 9

What is an assembler?

Answer 9

Turns assembly into machine language, including converting various labels and variables

Question 10

What does a Virtual Machine do?

Answer 10

Provides indirection between a high level language and assembly

Question 11

How are Virtual Machines implemented?

Answer 11

Stack Machine

Question 12

How are function calls represented in a VM?

Answer 12

All arguments are already on the stack. Add the return code address and other pointers. Reserve space for the local variables. Move the stack pointer and jump

Question 13

How are methods and constructors different from regular function calls?

Answer 13

They also either allocate space or add a “this” reference

Question 14

How are variables tracked in a compiler?

Answer 14

A linked list of Symbol tables that each go deeper into scope

Question 15

What does an operating system take care of?

Answer 15

Memory management, device input, output, strings, arrays, math, initializing everything above

Question 16

What is Godel’s Theorem of Incompleteness?

Answer 16

All consistent axiomatic formulations of number theory include undecidable propositions

OR

Any system sufficiently powerful to express arithmetic is either incomplete or inconsistent

Question 17

What was Hilbert’s program?

Answer 17

Split mathematics (basic strings) and meta-mathematics (defining statements about such strings) to develop absolute proofs that don’t depend on other systems

Question 18

How does Godel numbering work?

Answer 18

Assign Godel numbers to all operations, variables, statements, predicates, and sequences of statements using clever schemes of multiplying prime numbers so that they are all unique

Question 19

What is the halting problem? How can we prove it is undecidable?

Answer 19

Decision problem for whether a given program halts on a given input.

Proof by contradiction. Assume it exists. Create a new program that takes an input and runs that input on that program. Halt if it doesn’t and loop if it does. Give that program as an input to itself l, which leads to a contradiction.

Question 20

What is a convolutional neural network?

Answer 20

Apply a kernel across an image to aggregate data, which creates a filtered set of linear combinations of local feature. Run that through a neural net

Question 21

What is a Recurrent Neural Network?

Answer 21

Takes input and then feeds back into itself. It can take 1 or multiple inputs and generate 1 or multiple outputs. Good for sequential data or keeping memory

Question 22

What is a Recursive neural network?

Answer 22

Aggregates into a hierarchical structure.

Question 23

How is 3-SAT NP Complete?

Answer 23

3-SAT is NP because you can brute force it.

According to Cook-Levin, you can simulate a nondeterministic Turing Machine into SAT, and then SAT is reducible to 3-SAT

Question 24

What is Benford’s Law? Why does it happen?

Answer 24

In many real life datasets, the leading digit is likely to be small. This tends to apply to values across multiple orders of magnitude, especially power laws

Question 25

What does it mean for Problem A to be reducible to Problem B? What is an example?

Answer 25

We can convert Problem A into Problem B, so if we can solve Problem B, we can solve Problem A.

For example, we can reduce adding a list of numbers to the Sum of 2 numbers.

Question 26

What does it mean for Problem A to be NP Complete? What does it intuitively mean?

Answer 26

1. Problem A is in NP
2. For all NP problems B, B is poly-time reducible to A

NP Complete problems are the hardest NP problems, and you can use them to solve all NP problems.

Question 27

What does it mean for Problem A to be NP Hard?

Answer 27

For all NP problems B, B is poly-time reducible to A. This is the second condition of NP Complete.

Question 28

What are the three parts of a floating point number?

Answer 28

Sign, exponent, significand