Hasil untuk "Mathematics"

D. G. Zill, M. Cullen

Part One - Ordinary Differential Equations. 1. First Order Differential Equations. 2. Second Order Differential Equations. 3. The Laplace Transform. 4. Series Solutions. 5. Numerical Approximation Of Solutions. 6. Sturm-Liouville Theory, Eigenfunction Expansions And Special Functions. Part Two - Vectors And Linear Algebra. 7. Vectors And Vector Space. 8. Matrices, Determinants And Systems Of Linear Equations. 9. Eigenvalues And Diagonalization. Part Three - Systems Of Differential Equations And Qualitative Methods. 10. Linear Systems Of Differential Equations. 11. Non-linear Differential Equations And Qualitative Methods. Part Four - Vector Analysis. 12. Vector Differential Calculus. 13. Vector Integral Calculus. Part Five - Fourier Analysis And Boundary Value Problems. 14. Fourier Series And Integrals. 15. Fourier Transforms. 16. Partial Differential Equations And Boundary Value Problems. Part Six - Complex Analysis. 17. Complex Numbers And Complex Fractions. 18. Complex Integration. 19. Conformal Mappings And Some Applications.

S. Freeman, Sarah L. Eddy, Miles J. McDonough et al.

J. Kilpatrick, J. Swafford, B. Findell

Liping Ma

A. Schoenfeld

M. Abramowitz, I. Stegun, R. H. Romer

J. Crank

F. Natterer

H. Hethcote

P. Brown, S. D. Pietra, V. D. Pietra et al.

J. Westwater, H. G. Drickamer

Lawrence S. Kroll

C. Hirsch

K. Ribet, David Eisenbud

A. Collins, J. Brown, S. E. Newman

R. Graham, D. Knuth, Or Patashnik

Chen C. Chang, H. Keisler

Zhangir Azerbayev, Hailey Schoelkopf, Keiran Paster et al.

We present Llemma, a large language model for mathematics. We continue pretraining Code Llama on the Proof-Pile-2, a mixture of scientific papers, web data containing mathematics, and mathematical code, yielding Llemma. On the MATH benchmark Llemma outperforms all known open base models, as well as the unreleased Minerva model suite on an equi-parameter basis. Moreover, Llemma is capable of tool use and formal theorem proving without any further finetuning. We openly release all artifacts, including 7 billion and 34 billion parameter models, the Proof-Pile-2, and code to replicate our experiments.

Yousef Wardat, Mohammad A. Tashtoush, Rommel Alali et al.

This study aims to examine the perspectives of various stakeholders, such as students and educators, on the use of artificial intelligence in teaching mathematics, specifically after the launch of ChatGPT. The study adopts a qualitative case study approach consisting of two stages: content analysis of interviews and investigation of user experience. The first stage of the study shows that ChatGPT is recognized for its improved math capabilities and ability to increase educational success by providing users with basic knowledge of mathematics and various topics. ChatGPT can offer comprehensive instruction and assistance in the study of geometry, and the public discourse on social media is generally positive, with enthusiasm for the use of ChatGPT in teaching mathematics and educational settings. However, there are also voices that approach using ChatGPT in educational settings with caution. In the second stage of the study, the investigation of user experiences through three educational scenarios revealed various issues. ChatGPT lacks a deep understanding of geometry and cannot effectively correct misconceptions. The accuracy and effectiveness of ChatGPT solutions may depend on the complexity of the equation, input data, and the instructions given to ChatGPT. ChatGPT is expected to become more efficient in resolving increasingly complex mathematical problems. The results of this investigation propose a number of avenues for research that ought to be explored in order to guarantee the secure and conscientious integration of chatbots, especially ChatGPT, into mathematics education and learning.