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# System prepended metadata

title: Elliot Real Analysis Exam prep

---

Elliot Real Analysis Exam prep (exam: 08/01/24)
Lectures (1-30):
- 1 & 2: Recap on sets, and on logical deduction in mathematics
- 3a: Functions
- 3b & 4a: Bounds on subsets of $\mathbb{R}$
- 4b: Upper and lower bounds
- 5a: Maxima and minima
- 5b: Suprema and Infima
- 6: Topological structure of the real line
- 7a: Open and closed sets
- 7b & 8: Sequences and convergence
- 9a: Subsequences and the Bolzano-Weierstrass Theorem
- 9b: Cauchy convergence theorem
- 9c: Series
- 9d: Convergence of series
- 10a: Properties of series
- 10b & 11: Limits and continuity of functions
- 12 & 13 & 14: Continuity
- 15a: Classification of discontinuities
- 15b: Sequences and series of functions (inc. convergence)
- 16a: Series of functions
- 16b: The Weierstrass Test
- 17 & 18 & 19: Infinitestimal Calculus: Differentiation
- 20 & 21: Derivatives at local extrema, and the Mean Value Theorem
- 22 & 23: Continuously differentiable and twice differentiable functions
- 24: Infinitesimal Calculus, Part II: Integration
- 25: Riemann-integral
- 26: Analysis in higher dimensions
- 27a: Vectors in $\mathbb{R}^{p}$
- 27b: Open sets in $\mathbb{R}^{p}$
- 27c & 28: Convergence of sequences of vectors
- 29: Limits of multivariable functions
- 30: Partial derivatives and Jacobians

![Screenshot 2023-12-15 at 09.25.16](https://hackmd.io/_uploads/rk5sjqYUT.png)

**Plan**

17/12
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Self: Up to BW
Lesson: Go over proofs and work on exercises from up to BW
B: next 3/4 from above
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18/12

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Self:

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19/12
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Self: [https://drive.google.com/file/d/1dW9pHfOQYMK0fFAMUvS2Bg4Ol4qQUFHd/view?usp=share_link]
Lesson: Start at Dense Sets, finish at Series
HW:
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20/12
![Screenshot 2023-12-19 at 10.42.43](https://hackmd.io/_uploads/r1pnmgyDT.png)
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Self: Following proofs
4.18 C
4.26
4.28
4.30
Prop. 5.2
5.5
5.6
Lemma 5.8
Remark 5.10

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21/12
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Self: 
Lesson: Start at Series, finish at Continuity
HW:
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22/12
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Self:

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23/12
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Self:
Lesson: Start Continuity, finish at uniform continuity
HW:
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24/12
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Self:
Lessson: If we could complete up to The Weierstrass Test, 
HW:
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25/12
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Self:

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26/12
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Self:
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27/12
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28/12
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29/12
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30/12
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31/12
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Self:
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01/01
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Self:
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02/01
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Self:

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03/01
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Self:
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04/01
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Self:

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05/01
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Self:
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06/01
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07/01
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Self:
Lessson:
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08/01
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Exam
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