*Chris Sangwin*

- Published in print:
- 2013
- Published Online:
- December 2013
- ISBN:
- 9780199660353
- eISBN:
- 9780191748257
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199660353.003.0005
- Subject:
- Mathematics, Educational Mathematics

Mathematical notation has a long and interesting history. It also has a profound influence on the mind. For mathematical computer aided assessment (CAA) students must enter their answer into the ...
More

Mathematical notation has a long and interesting history. It also has a profound influence on the mind. For mathematical computer aided assessment (CAA) students must enter their answer into the machine. This chapter examines mathematical notation and its meaning. It considers syntax for typing expressions into a machine using a keyboard and other types of interactions.Less

Mathematical notation has a long and interesting history. It also has a profound influence on the mind. For mathematical computer aided assessment (CAA) students must enter their answer into the machine. This chapter examines mathematical notation and its meaning. It considers syntax for typing expressions into a machine using a keyboard and other types of interactions.

*Vlatko Vedral*

- Published in print:
- 2006
- Published Online:
- January 2010
- ISBN:
- 9780199215706
- eISBN:
- 9780191706783
- Item type:
- chapter

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199215706.003.0002
- Subject:
- Physics, Theoretical, Computational, and Statistical Physics

This chapter reviews all the rules of quantum mechanics and their mathematical notation. It also considers quantum entanglement, a fundamental resource in quantum information. There are four basic ...
More

This chapter reviews all the rules of quantum mechanics and their mathematical notation. It also considers quantum entanglement, a fundamental resource in quantum information. There are four basic postulates of quantum mechanics, that indicate how to represent physical systems, how to represent observations, how to carry out measurements, and how systems evolve when “not measured”. Before describing the laws of quantum mechanics, their mathematical background is first described, along with a Mach Zehnder interferometer experiment in which the (strange) readings on the detectors can be explained by quantum mechanics. This chapter also discusses the Dirac notation, qubits, Hilbert spaces, projective measurements and operations, unitary operations, eigenvectors and eigenvalues, spectral decomposition, applications of the spectral theorem, Dirac notation shorthands, and mixed states.Less

This chapter reviews all the rules of quantum mechanics and their mathematical notation. It also considers quantum entanglement, a fundamental resource in quantum information. There are four basic postulates of quantum mechanics, that indicate how to represent physical systems, how to represent observations, how to carry out measurements, and how systems evolve when “not measured”. Before describing the laws of quantum mechanics, their mathematical background is first described, along with a Mach Zehnder interferometer experiment in which the (strange) readings on the detectors can be explained by quantum mechanics. This chapter also discusses the Dirac notation, qubits, Hilbert spaces, projective measurements and operations, unitary operations, eigenvectors and eigenvalues, spectral decomposition, applications of the spectral theorem, Dirac notation shorthands, and mixed states.

*Peter J. Diggle and Amanda G. Chetwynd*

- Published in print:
- 2011
- Published Online:
- December 2013
- ISBN:
- 9780199543182
- eISBN:
- 9780191774867
- Item type:
- book

- Publisher:
- Oxford University Press
- DOI:
- 10.1093/acprof:oso/9780199543182.001.0001
- Subject:
- Mathematics, Probability / Statistics, Biostatistics

An antidote to technique-oriented service courses, this book studiously avoids the recipe-book style and keeps algebraic details of specific statistical methods to the minimum extent necessary to ...
More

An antidote to technique-oriented service courses, this book studiously avoids the recipe-book style and keeps algebraic details of specific statistical methods to the minimum extent necessary to understand the underlying concepts. Instead, it aims to give the reader a clear understanding of how core statistical ideas of experimental design, modelling, and data analysis are integral to the scientific method. Aimed primarily towards a range of scientific disciplines (albeit with a bias towards the biological, environmental, and health sciences), this book assumes some maturity of understanding of scientific method, but does not require any prior knowledge of statistics, or any mathematical knowledge beyond basic algebra and a willingness to come to terms with mathematical notation. Any statistical analysis of a realistically sized data-set requires the use of specially written computer software. An Appendix introduces the reader to our open-source software of choice. All of the material in the book can be understood without using either R or any other computer software.Less

An antidote to technique-oriented service courses, this book studiously avoids the recipe-book style and keeps algebraic details of specific statistical methods to the minimum extent necessary to understand the underlying concepts. Instead, it aims to give the reader a clear understanding of how core statistical ideas of experimental design, modelling, and data analysis are integral to the scientific method. Aimed primarily towards a range of scientific disciplines (albeit with a bias towards the biological, environmental, and health sciences), this book assumes some maturity of understanding of scientific method, but does not require any prior knowledge of statistics, or any mathematical knowledge beyond basic algebra and a willingness to come to terms with mathematical notation. Any statistical analysis of a realistically sized data-set requires the use of specially written computer software. An Appendix introduces the reader to our open-source software of choice. All of the material in the book can be understood without using either R or any other computer software.

*Joseph Mazur*

- Published in print:
- 2016
- Published Online:
- January 2018
- ISBN:
- 9780691173375
- eISBN:
- 9781400850112
- Item type:
- chapter

- Publisher:
- Princeton University Press
- DOI:
- 10.23943/princeton/9780691173375.003.0001
- Subject:
- Mathematics, History of Mathematics

This chapter traces the beginnings of mathematical notation. For tens of thousands of years, humans had been leaving signification marks in their surroundings, gouges on trees, footprints in hard ...
More

This chapter traces the beginnings of mathematical notation. For tens of thousands of years, humans had been leaving signification marks in their surroundings, gouges on trees, footprints in hard mud, scratches in skin, and even pigments on rocks. A simple mark can represent a thought, indicate a plan, or record a historical event. Yet the most significant thing about human language and writing is that speakers and writers can produce a virtually infinite set of sounds, declarations, notions, and ideas from a finite set of marks and characters. The chapter discusses the emergence of the alphabet, counting, and mathematical writing. It also considers the discovery of traces of Sumerian number writing on clay tablets in caves from Europe to Asia, the use of Egyptian hieroglyphics, and algebra problems in the Rhind (or Ahmes) papyrus that presented simple equations without any symbols other than those used to indicate numbers.Less

This chapter traces the beginnings of mathematical notation. For tens of thousands of years, humans had been leaving signification marks in their surroundings, gouges on trees, footprints in hard mud, scratches in skin, and even pigments on rocks. A simple mark can represent a thought, indicate a plan, or record a historical event. Yet the most significant thing about human language and writing is that speakers and writers can produce a virtually infinite set of sounds, declarations, notions, and ideas from a finite set of marks and characters. The chapter discusses the emergence of the alphabet, counting, and mathematical writing. It also considers the discovery of traces of Sumerian number writing on clay tablets in caves from Europe to Asia, the use of Egyptian hieroglyphics, and algebra problems in the Rhind (or Ahmes) papyrus that presented simple equations without any symbols other than those used to indicate numbers.