Mathematical works
This archive brings together the mathematical work I have published online so far, with every PDF hosted here for direct download. It includes my graduate research, published papers, master’s thesis, olympiad books, problem collections, historical drafts, and contest materials.
PDF collection
The collection is ordered newest first. Each entry identifies whether its date is a publication date, a document date, a draft date, or a contest date. Download totals count requests made through this page.
Showing 33 of 33 PDFs
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Research
Hosted arXiv version
A unified bibliography and summary of publications on comparative prime number theory. It was first posted to arXiv on September 15, 2023; this hosted v3 is dated December 11, 2024, and the journal article appeared in Expositiones Mathematicae in May 2025.
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Books
Draft dated
This incomplete 2023 draft is preserved for its development history. The completed version was first published in 2026. Its polynomial and trigonometry material has since been extensively researched, expanded, and completed as two full lesson books with complete solution manuals, also divided into five polynomial and seven trigonometry coursebooks. The trigonometry collection now follows thousands of years of mathematical history and develops the new Lyran Cuneiform Numeral System for base 60 (sexagesimal), base 70 (septuagesimal), and other bases through 99; larger bases are possible by extending the Sumerian-style symbol tradition.
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2023 incomplete draft2026 independently published books
Completed and expanded in 2026
The unfinished manuscript was substantially researched, rewritten, and expanded into five polynomial and seven trigonometry coursebooks. The same complete curriculum is also available as two lesson books with complete solution manuals. All 16 books are independently published by Amir Parvardi through Amazon KDP and available from Amazon.
View the independently published 2026 books
Olympiad Algebra Solutions Manual for Book 1
Paperback667 pages
KACY collection
11 contest PDFs · Booklet 1 of 11
Problem sets
Dated
The complementary review problems that did not fit into the original pool of 1,220 algebra problems.
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Research
Print issue
A Canadian Mathematical Bulletin paper strengthening bounds related to Burgess's classical result. It was first posted to arXiv on August 24, 2020, published online on January 13, 2021, and printed in Volume 65, Issue 1 in March 2022.
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Research
Thesis dated
Amir Parvardi's UBC master's thesis, dated August 2019, on representing residue classes through products of small integers. Its central result was developed with Greg Martin into Subproducts of Small Residue Classes, published online by the Canadian Mathematical Bulletin on January 13, 2021 and printed in its March 2022 issue.
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Books
Published
The first volume of a solved-problem series, with 175 functional equations and a concise introduction to the main techniques.
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Drafts
Demo dated
A demonstration edition containing selected problems from the 2015–2016 competition season.
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Books
Published
A self-contained number theory text with theory, worked examples, and olympiad problems from introductory to advanced level.
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Research
Hosted arXiv version
Joint work with Peyman Nasehpour on additive and modular functions over semiring-like structures. This hosted arXiv v1 is dated March 10, 2016; the article was published online by Communications in Algebra on December 15, 2017.
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Problem sets
Dated
A broad 2012 problem bank for regional and international olympiad number theory practice.
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Problem sets
Dated
A second short geometry set with source links to the original problem discussions.
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Problem sets
Dated
Fifty focused Diophantine-equation problems with solutions and links to related discussions.
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Problem sets
Dated
A compact 2011 collection drawn from the IMO, shortlists, longlists, and other established competitions.
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Problem sets
Dated
A source-indexed problem set originally posted through the Art of Problem Solving community in June 2011.
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Problem sets
Dated
A 2011 collection from the IMO, olympiad shortlists and longlists, and other competitions.
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Problem sets
Dated
A 2011 algebra collection for developing functional-equation technique through solved problems.
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Research
Dated
An elementary development of LTE and its applications to exponential Diophantine equations.
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Research
Dated
An earlier Academia record of the LTE article, preserved here with its publication history.
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Problem sets
Dated
A concise 2011 collection of polynomial problems with solutions for algebra training.
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Problem sets
Dated
Fifty-three trigonometry problems collected for olympiad practice in February 2011.
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Problem sets
Dated
A medium-to-hard geometry practice collection created in 2011, with complete solutions.
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Problem sets
Dated
Amir Parvardi's first compiled problem set, created in January 2011 for olympiad inequality practice.
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