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Inhaltsangabe
Most calculus is taught as if the symbols are the mathematics.
This book takes the opposite view: the symbols are not the mathematics—they are just a coordinate system describing something deeper.
A point is not a pair of numbers. A function is not a formula. A coordinate system is not reality. These are descriptions layered on top of geometric objects that exist independently of how we label them.
The goal of this book is to rebuild calculus from that distinction upward.
It focuses on separating objects from their representations: what remains invariant when coordinates change, what survives different descriptions, and what it actually means for something to be geometric rather than symbolic.
Along the way, familiar ideas from calculus are reframed in a coordinate-independent way, leading naturally toward the language of manifolds and differential geometry.
This is not a procedural textbook. It does not begin with memorization or computation tricks. It begins with meaning.
You will learn to see:
- why coordinates are optional rather than fundamental
- what “the same object” means under different descriptions
- how calculus changes when symbols stop being mistaken for structure
- the geometric foundation behind manifolds and curvature
The aim is not to make calculus more complicated, but to make it impossible to unsee what it is really doing.
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Paperback. Zustand: new. Paperback. Most calculus is taught as if the symbols are the mathematics.This book takes the opposite view: the symbols are not the mathematics-they are just a coordinate system describing something deeper.A point is not a pair of numbers. A function is not a formula. A coordinate system is not reality. These are descriptions layered on top of geometric objects that exist independently of how we label them.The goal of this book is to rebuild calculus from that distinction upward.It focuses on separating objects from their representations: what remains invariant when coordinates change, what survives different descriptions, and what it actually means for something to be geometric rather than symbolic.Along the way, familiar ideas from calculus are reframed in a coordinate-independent way, leading naturally toward the language of manifolds and differential geometry.This is not a procedural textbook. It does not begin with memorization or computation tricks. It begins with meaning.You will learn to see: why coordinates are optional rather than fundamentalwhat "the same object" means under different descriptionshow calculus changes when symbols stop being mistaken for structurethe geometric foundation behind manifolds and curvatureThe aim is not to make calculus more complicated, but to make it impossible to unsee what it is really doing. This item is printed on demand. Shipping may be from multiple locations in the US or from the UK, depending on stock availability. Bestandsnummer des Verkäufers 9798255942152
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Manifolds (Paperback)
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Paperback. Zustand: new. Paperback. Most calculus is taught as if the symbols are the mathematics.This book takes the opposite view: the symbols are not the mathematics-they are just a coordinate system describing something deeper.A point is not a pair of numbers. A function is not a formula. A coordinate system is not reality. These are descriptions layered on top of geometric objects that exist independently of how we label them.The goal of this book is to rebuild calculus from that distinction upward.It focuses on separating objects from their representations: what remains invariant when coordinates change, what survives different descriptions, and what it actually means for something to be geometric rather than symbolic.Along the way, familiar ideas from calculus are reframed in a coordinate-independent way, leading naturally toward the language of manifolds and differential geometry.This is not a procedural textbook. It does not begin with memorization or computation tricks. It begins with meaning.You will learn to see: why coordinates are optional rather than fundamentalwhat "the same object" means under different descriptionshow calculus changes when symbols stop being mistaken for structurethe geometric foundation behind manifolds and curvatureThe aim is not to make calculus more complicated, but to make it impossible to unsee what it is really doing. This item is printed on demand. Shipping may be from our UK warehouse or from our Australian or US warehouses, depending on stock availability. Bestandsnummer des Verkäufers 9798255942152
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Taschenbuch. Zustand: Neu. Neuware - Most calculus is taught as if the symbols are the mathematics.This book takes the opposite view: the symbols are not the mathematics-they are just a coordinate system describing something deeper.A point is not a pair of numbers. A function is not a formula. A coordinate system is not reality. These are descriptions layered on top of geometric objects that exist independently of how we label them.The goal of this book is to rebuild calculus from that distinction upward.It focuses on separating objects from their representations: what remains invariant when coordinates change, what survives different descriptions, and what it actually means for something to be geometric rather than symbolic.Along the way, familiar ideas from calculus are reframed in a coordinate-independent way, leading naturally toward the language of manifolds and differential geometry.This is not a procedural textbook. It does not begin with memorization or computation tricks. It begins with meaning.You will learn to see: - why coordinates are optional rather than fundamental- what 'the same object' means under different descriptions- how calculus changes when symbols stop being mistaken for structure- the geometric foundation behind manifolds and curvatureThe aim is not to make calculus more complicated, but to make it impossible to unsee what it is really doing. Bestandsnummer des Verkäufers 9798255942152
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