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1. How did mathematicians find the epsilon-delta definition of continuity? : Introduction to basic

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2. Why should we study abstract mathematics? : Construction of real numbers.

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- 1) Why should we study abstract mathematics? : Construction of real numbers.
  
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- Quiz(week 2)
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3. Why should we study abstract mathematics? : Finding totally new numbers.

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- 1) Why should we study abstract mathematics? : Finding totally new numbers.
  
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- Quiz(week 3)
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Week 04: Why are the polynomials of degree five not solvable? : Introduction to modern abstract ...

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Week 05: Solvability of ordinary differential equations.

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Week 06: Isoperimetric problem

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Week 07: what is infinite dimensional space, and where is it?

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Week 08: Why does Jacobian appear in the change of variables for multiple integrals?

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Week 09: I have trouble with eigenvaluse and eigenvectors. Why should I care?

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Week 10: Should I study math to become a fund manager? (Lagrange multiplier method)

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Week 11: Should I study math to become a quant? (Black-Scholes equation)

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Week 12: Should I study math to become an economist? (Brouwer’s fixed point theorem)

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Week 13: MATLAB Examples for Chapters 8 and 9

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Week 14: A taste for optimization

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