Research Lab Internship — Background Survey

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Name: _________
**Date:** _____________

There are no right or wrong answers. This helps us understand where you are starting from so we can make this week as useful as possible for you.

Part 1 — Mathematics Background

1. Which of the following topics have you studied? (Circle all that apply)

Algebra Calculus Statistics Probability Trigonometry Vectors Matrices Complex Numbers Proof by Induction Proof by Contradiction Graph Theory Combinatorics Number Theory Geometry

2. How would you rate your comfort with the following? (1 = never seen it, 5 = very confident)

Topic Rating (1–5)
Solving algebraic equations  
Writing a mathematical proof  
Understanding a proof written by someone else  
Counting arguments (combinatorics)  
Thinking about infinite processes or limits  

3. Have you encountered any of the following? (Circle if yes)

  • Pigeonhole principle
  • Mathematical induction
  • Graph theory / networks
  • Euler characteristic
  • Linear algebra (matrices, eigenvalues)
  • Cryptography (modular arithmetic)
  • Game theory

4. Describe a mathematical result, puzzle, or idea that you found genuinely surprising or beautiful (can be simple too don’t worry):

 

 

 

Part 2 — Programming and Computing

5. Do you have any programming experience?
☐ None ☐ A little (school projects / tutorials) ☐ Moderate (personal projects) ☐ Confident

6. If yes, which languages?

 

Part 3 — Interests and Goals

8. Which of the following best describes the kind of mathematics you enjoy most? (Rank 1–4, with 1 being your favorite)

__ Puzzles and games (finding clever tricks)
__ Applications (solving real-world problems)
__ Proofs and theory (understanding *why* things are true)
__ Computation (writing algorithms, exploring with code)

9. What draws you to mathematics or science as a subject?

 

 

10. Is there a specific research area or career path you are curious about?

 

 

11. What do you hope to get out of this internship?

 

 

12. Is there anything you are nervous or uncertain about coming into this internship?

 

 

Part 4 — Quick Aptitude Test

No pressure — attempt whatever you can. Skip freely. These are here so we know how to pace your experience in this program.

Q1. Have you ever read a research paper before? Which one was it, if so? Explain.

 

 

 

Q2. What does the term “literature review” mean to you?

 

 

 

 

Q3. When you hear the word “Network” or “Graph” in a math or computer science context, what visual comes to your mind?

 

 

 

 

Q4. In a 4-person group project that involves reading papers, writing papers, analyzing data, and designing visuals/presentations, which role do you naturally gravitate towards and why?

 

 

 

 

Q5 (Open-ended). Is there an idea within Computer Science (any subfield) that has always interested you, which you want to dive deep into for research?

 

 

 

 

Thank you! We’ll collect these and use them to shape the week.

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