Sign Patterns of J-orthogonal Matrices

This thesis builds upon the results in “G-matrices, J-orthogonal matrices, and their sign patterns”, Czechoslovak Math. J. 66 (2016), 653-670, by Hall and Rozloˇzn ́ık. Some general results about the sign patterns of J-orthogonal matrices are proved, including about block diagonal matrices. It is shown that every full 4 × 4 sign pattern allows J -orthogonality and as a result that, for n ≤ 4, all n × n full sign patterns allow a J-orthogonal matrix as well as a G-matrix. The 3 × 3 sign patterns of the J -orthogonal matrices which have zero entires are also characterized

Pay Toll with Coins: Looking Back on FBAR Penalties and Prosecutions to Inform the Future of Cryptocurrency Taxation

Cryptocurrencies are gaining a foothold in the globaleconomy, and the government wants its cut. However, fewpeople are reporting cryptocurrency transactions on their taxreturns. How will the IRS solve its cryptocurrencynoncompliance problem? Its response so far bears manysimilarities to the government’s campaign to increase Reportsof Foreign Bank and Financial Accounts (FBARs). FBARnoncompliance penalties are notoriously harsh, and thegovernment has pursued them vigorously. This Note exploresthe connections and differences between cryptocurrencyreporting and foreign bank account reporting in an effort topredict the future regime of cryptocurrency tax compliance

Sign patterns of J-orthogonal matrices

This paper builds upon the results in the article “G-matrices, J-orthogonal matrices, and their sign patterns", Czechoslovak Math. J. 66 (2016), 653-670, by Hall and Rozloznik. A number of further general results on the sign patterns of the J-orthogonal matrices are proved. Properties of block diagonal matrices and their sign patterns are examined. It is shown that all 4 × 4 full sign patterns allow J-orthogonality. Important tools in this analysis are Theorem 2.2 on the exchange operator and Theorem 3.2 on the characterization of J-orthogonal matrices in the paper “J-orthogonal matrices: properties and generation", SIAM Review 45 (3) (2003), 504-519, by Higham. As a result, it follows that for n ≤4 all n×n full sign patterns allow a J-orthogonal matrix as well as a G-matrix. In addition, the 3 × 3 sign patterns of the J-orthogonal matrices which have zero entries are characterized

Adapting to Trig: Using the ALEKS Adaptive Technology to Improve Students’ Learning and Retention in A College Trigonometry Course

The Department of Mathematics and Statistics at Georgia State University has recently introduced the MATH 1112 “College Trigonometry” course designed to prepare students in several STEM majors for Calculus courses. This project received STEM funds to introduce the paradigm of individualized adaptive learning, offered by the ALEKS online platform, into teaching of College Trigonometry at GSU. The key objectives of the proposed work are: To incorporate the ALEKS adaptive learning technology into the College Trigonometry course. The project team designed a comprehensive course program that included both trigonometry topics and review topics necessary for students’ success in the current and future courses. By its inherent design, ALEKS software automatically generated individualized learning paths for each student, reintroducing earlier topics and review topics as necessary. To facilitate self directed learning initiatives by capitalizing on the adaptive nature of ALEKS’s individualized learning paths, which places more responsibility on students to plan their work outside of class. We offered students additional guidance and tutoring support by making a lab space with a dedicated GTA available to them. To enhance the use of technology in the course by developing supplemental demonstrations using CAS. At all stages, we collected both qualitative and quantitative data on students’ learning and attitudes

Incorporating “Just in Time” Teaching to Enhance the Lecture/Recitation Format in Calculus

The Department of Mathematics and Statistics at Georgia State University has recently switched MATH 2211/2212 to three hours of lecture and one hour of recitation instead of four hours of lecture weekly. This has left Calculus instructors with some difficulty adapting to less lecture time each week. This project was supported by STEM funds to prepare a major overhaul of the Calculus sequence at GSU to better fit the newly changed lecture/recitation format. The key objectives of the proposed work are: To incorporate “Just in Time” teaching methods to make more efficient use of the reduced lecture time. By preparing in advance a comprehensive set of review materials and pre-quizzes, we attempted to encourage students to do more preparation ahead of time making lectures more helpful and efficient. To enhance the use of technology in our instruction of Calculus by developing supplemental demonstrations using CAS. We focused on the more challenging topics, so that less class time was required to gain understanding of these difficult concepts. We made these available in advance to supplement other “Just in Time” materials. At all stages, we collected both qualitative and quantitative data on students’ learning and attitudes