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Mathematics, Matter and Method

Hilary Putnam • Cambridge University Press eBooks (1979)

Introduction 1. Truth and necessity in mathematics 2. The thesis that mathematics is logic 3. Mathematics without foundations 4. What is mathematical truth? 5. Philosophy of physics 6. An examination of Grunbaum's philosophy of geometry 7. ...

OPENALEX DOI: https://doi.org/10.1017/cbo9780511625268

Mathematical Objectivity and Mathematical Objects

Hartry H. Field • Oxford University Press eBooks (2001)

Abstract Focuses on an issue about the objectivity of mathematics—the extent to which undecidable sentences have determinate truth‐value—and argues that this issue is more important than the issue of the existence of mathematical objects. I...

OPENALEX DOI: https://doi.org/10.1093/0199242895.003.0011

Mathematics in Population Biology

Horst R. Thieme • Princeton University Press eBooks (2003)

"The formulation, analysis, and re-evaluation of mathematical models in population biology has become a valuable source of insight to mathematicians and biologists alike. This book presents an overview and selected sample of these results a...

OPENALEX DOI: https://doi.org/10.1515/9780691187655

DAF-UNet: Deformable U-Net with Atrous-Convolution Feature Pyramid for Retinal Vessel Segmentation

Yongchao Duan, Rui Yang, Ming Zhao, Mingrui Qi et al. • Mathematics (2025)

Segmentation of retinal vessels from fundus images is critical for diagnosing diseases such as diabetes and hypertension. However, the inherent challenges posed by the complex geometries of vessels and the highly imbalanced distribution of ...

DOAJ Open Access (DOAJ) DOI: 10.3390/math13091454

System 2 Thinking in OpenAI’s o1-Preview Model: Near-Perfect Performance on a Mathematics Exam

Joost C. F. de Winter, Dimitra Dodou, Yke Bauke Eisma • Computers (2024)

The processes underlying human cognition are often divided into System 1, which involves fast, intuitive thinking, and System 2, which involves slow, deliberate reasoning. Previously, large language models were criticized for lacking the de...

DOAJ Open Access (DOAJ) DOI: 10.3390/computers13110278

Graded weakly 1-absorbing prime ideals

Ünsal Tekir, Suat Koç, Rashid Abu-Dawwas, Eda Yıldız • Cubo (2022)

In this paper, we introduce and study graded weakly 1-absorbing prime ideals in graded commutative rings. Let $G$ be a group and $R$ be a $G$-graded commutative ring with a nonzero identity $1\neq0$. A proper graded ideal $P$ of $R$ is call...

DOAJ Open Access (DOAJ) DOI: 10.56754/0719-0646.2402.0291

Mathematical Statistics

Keith Knight • Chapman & Hall/CRC eBooks (1999)

Traditional texts in mathematical statistics can seem - to some readers-heavily weighted with optimality theory of the various flavors developed in the 1940s and50s, and not particularly relevant to statistical practice. Mathematical Statis...

OPENALEX DOI: https://doi.org/10.1201/9780367805319

Mathematical Capabilities of ChatGPT

Simon Frieder, Luca Pinchetti, Chevalier Chevalier, Ryan-Rhys Griffiths et al. • neural information processing systems (2023)

We investigate the mathematical capabilities of two iterations of ChatGPT (released 9-January-2023 and 30-January-2023) and of GPT-4 by testing them on publicly available datasets, as well as hand-crafted ones, using a novel methodology. In...

OPENALEX Open Access DOI: https://doi.org/10.52202/075280-1205

Mathematics without Numbers

Geoffrey Paul Hellman (1993)

Abstract Develops a structuralist understanding of mathematics, as an alternative to set‐ or type‐theoretic foundations, that respects classical mathematical truth while minimizing Platonist commitments to abstract entities. Modal logic is ...

OPENALEX DOI: https://doi.org/10.1093/0198240341.001.0001

Advanced Engineering Mathematics

Ken A. Stroud, Dexter J. Booth (2011)

A long-standing, best-selling, comprehensive textbook covering all the mathematics required on upper level engineering mathematics undergraduate courses. Its unique programmed approach takes students...

OPENALEX DOI: https://doi.org/10.1057/978-0-230-34474-7

Mathematics and the Body

Elizabeth de Freitas, Nathalie Sinclair • Cambridge University Press eBooks (2014)

This book explores alternative ways to consider the relationship between mathematics and the material world. Drawing on the philosophy of Gilles Châtelet and the post-humanist materialism of Karen Barad, the authors present an 'inclusive ma...

OPENALEX DOI: https://doi.org/10.1017/cbo9781139600378

On Mathematical Problem Posing.

Edward A. Silver • for the learning of mathematics (1994)

In mathematics classes at all levels of schooling in all countries of the world, students can be observed solving problems. The quality and authenticity of these mathematics problems has been the subject of many discussions and debates in r...

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Mathematics for Economists

Carl G. Simon, Lawrence E. Blume (1994)

An abundance of applications to current economic analysis, illustrative diagrams, thought-provoking exercises, careful proofs, and a flexible organization-these are the advantages that Mathematics for Economists brings to today's classroom....

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The Mathematics of Financial Derivatives

Paul Wilmott, Sam Howison, Jeff Dewynne • Cambridge University Press eBooks (1995)

Finance is one of the fastest growing areas in the modern banking and corporate world. This, together with the sophistication of modern financial products, provides a rapidly growing impetus for new mathematical models and modern mathematic...

OPENALEX DOI: https://doi.org/10.1017/cbo9780511812545