MAT 401 Real Analysis
Undergraduate course, Mathematics Department, Utica College, 2019
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Special Information, Mathematics Department, Utica College, 2020
MAT 151 Precalculus
Undergraduate course, Mathematics Department, Utica College, 2020
MAT 201 Calculus 1
Undergraduate course, Mathematics Department, Utica College, 2020
MAT 151 Precalculus
Undergraduate course, Mathematics Department, Utica College, 2020
MAT 201 Calculus 1
Undergraduate course, Mathematics Department, Utica College, 2020
MAT 151 Precalculus
Undergraduate course, Mathematics Department, Utica College, 2021
MAT 201 Calculus 1 (Online)
Undergraduate course, Mathematics Department, Utica College, 2021
MAT 201 Calculus 1 (On ground)
Undergraduate course, Mathematics Department, Utica College, 2021
MAT 401 Real Analysis
Undergraduate course, Mathematics Department, Utica College, 2021
MAT 201 Calculus 1
Undergraduate course, Mathematics Department, Utica College, 2021
MAT 334 Introduction to Abstract Algebra
Undergraduate course, Mathematics Department, Utica College, 2021
MAT 151 Precalculus
Undergraduate course, Mathematics Department, Utica University, 2023
MAT 201 Calculus 1
Undergraduate course, Mathematics Department, Utica University, 2023
MAT 401 Real Analysis
Undergraduate course, Mathematics Department, Utica University, 2023
MAT 201 Calculus 1 - Utica Science Academy
Undergraduate course, Mathematics Department, Utica University, 2023
MAT 201 Calculus 1 - Utica University
Undergraduate course, Mathematics Department, Utica University, 2023
MAT 351 Euclidean and Non-Euclidean Geometry
Undergraduate course, Mathematics Department, Utica University, 2023
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MAT 151 Precalculus
Undergraduate course, Mathematics Department, Utica College, 2021
Posts
portfolio
publications
Computing isomorphism numbers of F-crystals using the level torsions
Journal of Number Theory, 2012
In this paper, we use the level torions to compute isomorphism numbers of various F-crystals.
Subtle invariants of F-crystals
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.
Minimal F-crystals and isomorphism numbers of isosimple F-crystals
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.
Finding a unique solution to Radon-Kaczmarz puzzles
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.
Dimensions of automorphism group schemes of finite level truncation of F-cyclic F-crystals
Transactions of the American Mathematical Society, 2021
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.
The Number Line through Guided Inquiry
MAA Press: An Imprint of the American Mathematical Society, 2022
This is a real analysis textbook for future secondary teachers and general undergraudate mathematics major. This is a joint work with David M. Clark.
Arithmetic Partial Derivative
Journal of Integer Sequences, 2022
In this paper, we investigate the dynamical system of higher order of arithmetic partial derivatives. We show that there are infinitely many numbers with exactly n anti-partial derivatives for any nonnegative integer n. This is a joint work with Brad Emmons.
talks
teaching
Guidelines for letters of recommendation
General advice, Mathematics Department, Utica University, 2022
This page contains advice for people asking for a letter of recommendation from me (or someone like me).
MAT 151 Precalculus
Undergraduate course, Mathematics Department, Utica University, 2024
Welcome to the home page of Dr. Xiao Xiao’s Precalculus course at Utica University. You can find all the information and documents for this course on this page. Please check this page frequently for announcements and assignments.
MAT 201 Calculus 1
Undergraduate course, Mathematics Department, Utica University, 2024
Welcome to the home page of Dr. Xiao Xiao’s Calculus 1 course at Utica University. You can find all the information for this course on this page. Please check this page frequently for announcements and assignments.
MAT 341 Number Theory
Undergraduate course, Mathematics Department, Utica University, 2024
Welcome to the home page of Prof. Xiao Xiao’s Number Theory course at Utica University. You can find all the informtion and documents for this course on this page. Please check this page frequently for announcements and assignments.