mathematical foundations

USAGE SUMMARY

The phrase "mathematical foundations" is correct and usable in written English.
You can use it when you are discussing a mathematical concept or system and its foundations. For example: "The mathematical foundations of calculus have been studied for centuries."

✓ Grammatically correct

Science

Academia

News & Media

Human-verified examples from authoritative sources

Exact Expressions

60 human-written examples

Those we applied are well documented in graph theory, the area of mathematics that deals with the mathematical foundations of networks.

Biology Direct

On The Mathematical Foundations of Learning.

Massachusetts Institute of Technology

Mathematical Foundations of Computer Science pages 1 20 (2003).

Nature

Mathematical foundations and practical implementation of the method are discussed.

Journal of Sound and Vibration

Provides mathematical foundations underlying the theory of operations management.

Massachusetts Institute of Technology

Sean Rice, Evolutionary Theory: Conceptual and Mathematical Foundations.

Massachusetts Institute of Technology

Certainly the grammar of music – rhythm and pitch – has mathematical foundations.

The Guardian - Music

In the 1960's, Dr. Arens shifted his focus to the mathematical foundations of physics.

The New York Times

But certain aspects of their mathematical foundations are also strikingly similar.

Nature

His textbook "Mathematical Foundations for Social Analysis" (Bobbs-Merrill, 1965) described the mathematical underpinnings for such analyses.

The New York Times

Wheeler, J. A. in Mathematical Foundations of Quantum Theory (eds Marlow, A.R.) 9 48 (Academic Press, 1978).

Nature

Expert writing Tips

Best practice

When discussing the "mathematical foundations" of a field, be specific about which mathematical concepts are most relevant. This adds clarity and depth to your analysis.

Common error

Avoid using "mathematical foundations" as a vague reference to all mathematical principles. Instead, focus on the specific mathematical theories and axioms that are essential to the topic you're discussing.

Linguistic Context

The phrase "mathematical foundations" functions as a noun phrase, typically serving as the subject or object of a sentence. It refers to the basic principles, axioms, and concepts that underpin a mathematical theory or a field of study. As Ludwig AI confirms, the phrase is correct and usable.

Expression frequency: Very common

Frequent in

Academia

40%

Science

40%

News & Media

20%

Less common in

Wiki

0%

Encyclopedias

0%

Formal & Business

0%

Ludwig's WRAP-UP

In summary, "mathematical foundations" is a grammatically correct and frequently used noun phrase referring to the fundamental principles and concepts underlying mathematics and related fields. Ludwig AI confirms its validity. Its use is common in academic, scientific, and technical contexts. When using this phrase, be specific about the particular mathematical concepts to provide clarity and depth. Alternatives such as "mathematical principles" and "mathematical basis" can be used depending on the specific nuance you wish to convey. Understanding its proper usage ensures clear and effective communication in technical and academic discussions.

More alternative expressions

Phrases that express similar concepts, ordered by semantic similarity:

mathematical principles

Replaces "foundations" with "principles", focusing on the core tenets rather than the structural basis.

mathematical basis

Substitutes "foundations" with "basis", emphasizing the core support or reason.

mathematical underpinnings

Uses "underpinnings" instead of "foundations", highlighting the supporting structure from below.

mathematical fundamentals

Replaces "foundations" with "fundamentals", focusing on essential skills and knowledge.

mathematical framework

Replaces "foundations" with "framework", focusing on the structural system.

mathematical groundwork

Similar to "foundations", emphasizing the initial work to establish the concepts.

theoretical mathematics

Shifts the focus to the theoretical aspects of mathematics, implying the foundational elements.

core mathematical concepts

Focuses on essential concepts instead of the entire foundational structure.

fundamental mathematical concepts

Highlights the essential and basic ideas of mathematics.

mathematical infrastructure

Uses "infrastructure" metaphorically to indicate the underlying support system.

FAQs

How can I use "mathematical foundations" in a sentence?

You can use "mathematical foundations" to refer to the basic principles and concepts upon which a mathematical theory or a field of study is built. For example, "A solid understanding of the "mathematical foundations" is crucial for advanced study in physics".

What are some alternatives to "mathematical foundations"?

Some alternatives include "mathematical principles", "mathematical basis", or "mathematical underpinnings" depending on the context.

Why is understanding the "mathematical foundations" important?

Understanding the "mathematical foundations" provides a strong base for further learning and application in related fields. It ensures a deeper comprehension of the underlying concepts and allows for more effective problem-solving.

What fields rely heavily on "mathematical foundations"?

Fields such as computer science, physics, engineering, and economics rely heavily on "mathematical foundations". These foundations provide the necessary tools and frameworks for modeling, analysis, and prediction in these disciplines.