MAT 401 Real Analysis
Undergraduate course, Mathematics Department, Utica College, 2019
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MAT 151 Precalculus
Undergraduate course, Mathematics Department, Utica College, 2020
MAT 201 Calculus 1
Undergraduate course, Mathematics Department, Utica College, 2020
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Computing Isomorphism Numbers of F-crystals Using the Level Torsions
Available at Journal of Number Theory, 2012
In this paper, we use the level torions to compute isomorphism numbers of various F-crystals.
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Subtle Invariants of F-crystals
Available at Journal of Ramanujan Mathematical Society, 2014
In this paper, we prove Vasiu’s conjecture that the isomorphism number of an F-crystal is equal to its level torsion.
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Minimal F-crystals and Isomorphism Numbers of Isosimple F-crystals
Available at Mathematische Nachrichten, 2017
In this paper, we generalize minimal p‐divisible groups to minimal F-crystals. Using minimal heights, we give an estimate of isomorphism number of isosimple F-crystals.
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Finding a Unique Finding a Unique Solution to Radon-Kaczmarz Puzzles
Available at Pi Mu Epsilon Journal, 2018
In this paper, we determine the size of a Radon-Kaczmarz Puzzle so that it has a unique solution when give a fixed set of clues. This is a joint work with Steven Rossi.
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Dimensions of Automorphism Group Schemes of Finite Level Truncation of F-Cyclic F-Crystals
Available at To appear in Transactions of the American Mathematical Society, 2019
In this paper, we develop a combinatorial formual to calculate the dimension of the automorphism group of F-cyclic F-crystal over an algebraically close dfield at some finite level. This is a joint work with Zeyu Ding.
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MAT 151 Precalculus
Undergraduate course, Mathematics Department, Utica College, 2020
Welcome to the home page of Dr. Xiao Xiao’s Precalculus course at Utica College. You can find all the information and documents for this course on this page. Please check this page frequently for announcements and assignments. Note that due to the COVID-19 pandemic, this course will be entirely online for the Fall 2020 semester.
MAT 201 Calculus 1
Undergraduate course, Mathematics Department, Utica College, 2020
Welcome to the home page of Dr. Xiao Xiao’s Calculus 1 course at Utica College. You can find all the information and documents for this course on this page. Please check this page frequently for announcements and assignments. Note that due to the COVID-19 pandemic, this course will be entirely online for the Fall 2020 semester.