What is Expositio?
A public repository for expository academic papers, with an integrated scholarly record.
Expositio is a place to read and cite expository work. Papers are published as stable,
citable records, while remaining connected to later versions, editorial decisions,
and related context.
Some papers are early drafts; others have been peer reviewed or formally published.
Each paper remains readable on its own, while preserving the history behind it.
The result is both a reading room and a record: a place to browse by field, read
papers in stable form, and follow their development over time.
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In this paper, we will prove a few different versions of the Central Limit Theorem: first,
a weak one, then the Lindeberg and Liapunov Central Limit Theorems. Additionally, we
will show the Central Limit Theorem in action and explain why it is one of the most useful
theorems …
Mathematics / Probability theory and stochastic processes
Mathematics / Statistics
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The circle method was first used by Hardy and Ramanujan in 1918 to investigate the
asymptotic growth of the partition function, which counts the number of ways to write n
as a sum of positive integers. This expository paper shows two examples of how Rademacher used a variant …
Mathematics / Number theory
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These are notes from two talks about Brauer groups, which present some selected results. The first talk focused on what is a Brauer group, in topological and algebraic settings, and their connection to cohomology. The second discusses Brauer groups of Henselian rings and the A…
Mathematics / Associative rings and algebras
Mathematics / Algebraic geometry
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These notes answer the question “How does the classical theory of modular forms connect with
the theory of automorphic forms on \(\operatorname{GL}_2\)?” They are a more detailed version of talks given at a student reading group based on Jacquet and Langland’s book. They were …
Mathematics / Number theory
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Let H(x) = x^6 + 2x^5 + 2x^4 + 2x^3 + x^2 + 1 be the sextic polynomial that parametrizes the primitive (2,3)-Misiurewicz points of the quadratic family f_c(z) = z^2 + c; equivalently, H is the degree-six factor of a_5(c) - a_2(c) (where a_0 = 0, a_{k+1} = a_k^2 + c) remaining af…
Mathematics / Number theory
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In this note, we discuss Euler's proof of the pentagonal number theorem and his related work on the subject. We also give Franklin's combinatorial proof as well as several problems that extend the results discussed in the note.
Mathematics / History and biography
Mathematics / Combinatorics
