Beginning Fall 2025
Apply Now!
Mathematics
Student Focused
We have a wide offering of general education courses designed to prepare you to major in Business and STEM (Science, Technology, Engineering, and Mathematics) fields.
$10M In Active Grants
We have dynamic research faculty who are
constantly striving for what is NEXT.
constantly striving for what is NEXT.
NEXT in Math
Promotion from Assistant Professor to Associate Professor & Tenure
Will Boney, Jake Fillman, & Wade Hindes
Promotion from Associate Professor to Professor
Jennifer Czocher, Samuel Obara, Ray Treinen, & Yong Yang
@TXST Math
- Location:
- Derrick 328 & Zoom
- Cost:
- Free
- Contact:
- nestor@txstate.edu
- Campus Sponsor:
- Department of Mathematics
This work explores the differential geometric structure of the family of 1-dimensional normal distributions, specifically the Poincaré Upper Half Plane structure arising from the Fisher-Information metric. The commonly applied Cramér-Rao lower bound reflects this metric’s decreasing nature, which is also connected to the differential geometric interpretation of the Schwarz-Pick lemma in the Poincaré Disk within complex analysis. In this presentation, we aim to extend the insights derived from the Poincaré Disk to bounded domains in C^n , treating these domains as statistical models. By establishing a correspondence between the Bergman metric and the Fisher-Information metric, we demonstrate a natural decreasing property. Additionally, we show that an equality condition between two Bergman metrics aligns with the identification of sufficient statistics. This framework also provides a robust approach for studying parametrized quantum circuits as statistical models for both pure and mixed quantum states, with potential applications in quantum computing. This work is a collaborative effort with J. Yum.
Click here for more information
more about event
- Location:
- Derrick 333 and Zoom
- Cost:
- Free
- Contact:
- vi11@txstate.edu
- Campus Sponsor:
- Department of Mathematics
Model diagnostics is an indispensable component in regression analysis, yet it has not been well addressed in generalized linear models (GLMs). When outcome data are discrete, classical Pearson and deviance residuals have limited utility in generating diagnostic insights. This paper establishes a novel diagnostic framework for GLMs and their extensions. Unlike the convention of using a point statistic as a residual, we propose to use a function as a vehicle to retain residual information. In the presence of data discreteness, we show that such a functional residual is appropriate for summarizing the residual randomness that cannot be captured by the structural part of the model. We establish its theoretical properties, which lead to the innovation of new diagnostic tools including the functionalresidual-vs-covariate plot and Function-to-Function plot (similar to a Quantile-Quantile plot). Our numerical studies demonstrate that the use of these tools can reveal a variety of model misspecifications, such as not properly including a higher-order term, an explanatory variable, an interaction effect, a dispersion parameter, or a zero-inflation component. As a general notion, the functional residual considerably broadens the diagnostic scope as it applies to GLMs for binary, ordinal and count data as well as semiparametric models (e.g., generalized additive models), all in a unified framework. Its functional form provides a way to unify point residuals such as Liu-Zhang’s surrogate residual and Li-Shepherd’s probability-scale residual. As its graphical outputs can be interpreted in a similar way to those for linear models, our framework also unifies diagnostic interpretation for discrete data and continuous data.
more about event
Meeting ID 863 7686 1836 Passcode SS_DERR333
https://txstate.zoom.us/j/86376861836?pwd=MuhOetE19T5FEcaby8gqQ3TlZD6PZa.1
Click here for more informationMath Education Seminar - Student-Generated Connections Across Contexts: Equivalence and Substitution
–
- Location:
- Zoom
- Cost:
- Free
- Contact:
- codypatterson@txstate.edu
- Campus Sponsor:
- Department of Mathematics
The concept of equivalence is fundamental to problem-solving in mathematics. Particularly, an oft-utilized feature of equivalence is substitution, in which the mathematics doer replaces one object with an equivalent object. Equivalence in general, and substitution in particular, have been identified as common threads that can tie together different areas of mathematics, but do students notice these connections in their own mathematics? In this talk, I report on task-based clinical interviews with students exploring the commonalities they identify among tasks implicitly involving equivalence relations. In particular, I discuss themes that students explicitly identified as relevant when answering the interview tasks: (1) substitution equivalence and (2) a distinction between students using a known equivalence for substitution or introducing their own equivalence.
Zoom
txstate.zoom.us… Click here for more information
more about event
Zoom
txstate.zoom.us… Click here for more information
- Location:
- DERR 338
- Cost:
- Free
- Contact:
- Tim Chase tmc113@txstate.edu
Cameron Farnsworth clf129@txstate.edu - Campus Sponsor:
- Department of Mathematics
Love a good problem? Like to solve difficult puzzles?
Join professors, graduate students and undergraduates as we tackle problems presented from several mathematical journals. An interest in higher level mathematics is all that is required to join our round table. Offer what you know, learn what you don't in a relaxed environment with some of our department's finest!
Join professors, graduate students and undergraduates as we tackle problems presented from several mathematical journals. An interest in higher level mathematics is all that is required to join our round table. Offer what you know, learn what you don't in a relaxed environment with some of our department's finest!