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I'm preparing my masters thesis in mathematics (Stochastic Calculus).

My first chapter consists of recalling some concepts like

  1. Hölder's inequality.

  2. Clarke's generalized gradient.

  3. Grönwall's inequality

  4. Convex functions.

What is a proper name for this chapter ? I went with Useful Theorems but it felt somewhat different than what I'm used to see in books.

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    I think this question might be opinion-based. Personally, I think something like "mathematical preliminaries" is suitable.
    – Galen
    May 15 at 21:03
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    @Galen Thanks ! That's a good title for it. It's about optimal control in markovian switching stochastic systems.
    – Hamdiken
    May 15 at 21:06
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    If you call the first chapter "Useful Theorems", what does that suggest about the theorems in the rest of the thesis?
    – Andreas Blass
    May 15 at 22:43
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    "Chapter 1 : I am born". OK, not original and possibly more detail than needed. Fallback to "Introduction" which sounds like a good way to start an ... introduction ? Or put another way, I think you're overthinking this.
    – StephenG - Help Ukraine
    May 16 at 1:47
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    Preliminaries or just Introduction.
    – markvs
    May 16 at 11:07

3 Answers 3

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A standard way to go is to write "Preliminaries" and give the definitions, notations, theorems, etc. which you use throughout the thesis.

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    Or Preliminaries or Introduction or Overview.
    – Jon Custer
    May 15 at 23:17
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    Another common option, along these lines, is “Background”
    – PLL
    May 16 at 8:03
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    @JonCuster I'm in a different field (Physics/Spectroscopy/Semiconductors) but I would expect this to be the chapter after the introduction. E.g. my PhD thesis "Introduction" was 4 pages of scene-setting with no equations or figures; that was followed by "Theoretical Background" - 40 pages with plenty of maths and diagrams. I'd expect both chapters to be shorter in a Master's thesis of course.
    – Chris H
    May 16 at 8:29
  • Preliminaries, Introduction, or Overview are all fine, depending on contents. // Establish notation. State theorems you will use, but without proof (unless method of proof is closely related the main part of the thesis). This chapter will probably not be repeated in any related papers you'll submit. // Start 2nd chapter with new material in a form that will be easy to condense for publication. (Important elements of proofs in the main part of the chapter (details in notes at end). You are not writing a textbook, but motivating, stating, proving new things.
    – BruceET
    May 17 at 6:51
  • It's not really the preliminaries of OP's work, those are very-well-established and very-widely-applicable definitions and results.
    – einpoklum
    May 17 at 13:15
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A somewhat standard structure would be:

  1. Introduction - explain what are you trying to accomplish and why it is important

  2. Background and related work - briefly explain all key concepts that the reader needs to know to understand your thesis

..followed by methods/proofs/results/analysis/discussion

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It may be worthwhile to separate to some extent two sorts of "background". One sort is the background and context needed to understand what you've done, and why you'd want to do it, and why it's progress... The other sort (obviously with overlap), is the background to understand the guts/proofs/... of your work.

It is often a mistake to combine the two... somehow in the mistaken belief that perfect logical order is necessary... or something.

So one could have "context/background", as well as "technical prerequisites"... Some readers might appreciate your making the distinction.

... and my joke-analogue is that to explain to someone why an automatic transmission may be better than a manual, and what's involved, ... FIRST say "ok, so you know about the Carnot cycle?" ...

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