Advanced Calculus
E639091
Advanced Calculus is a rigorous upper-level mathematics textbook by Lynn Harold Loomis (later revised by Shlomo Sternberg) that develops multivariable calculus and analysis with a strong emphasis on proofs and theoretical foundations.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Advanced Calculus canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T7047121 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Advanced Calculus Context triple: [Lynn Harold Loomis, notableWork, Advanced Calculus]
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A.
Functional Analysis: Introduction to Further Topics in Analysis
"Functional Analysis: Introduction to Further Topics in Analysis" is an advanced graduate-level textbook by Elias Stein that develops modern functional analysis with applications to areas such as operator theory, harmonic analysis, and partial differential equations.
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B.
Master of Mathematics (M.Math.)
The Master of Mathematics (M.Math.) is a highly rigorous postgraduate program in advanced mathematics, known for its strong theoretical foundation and emphasis on research-oriented training.
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C.
Mueller calculus
Mueller calculus is a mathematical framework in polarization optics that uses matrix operations to describe how optical elements transform the Stokes parameters of light.
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D.
Calculus Made Easy
Calculus Made Easy is a classic introductory mathematics book that simplifies and demystifies the fundamental concepts of calculus for beginners.
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E.
Principles of Mathematics
Principles of Mathematics is Bertrand Russell’s foundational work in mathematical logic and the philosophy of mathematics, arguing that mathematics can be derived from purely logical principles.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Advanced Calculus Target entity description: Advanced Calculus is a rigorous upper-level mathematics textbook by Lynn Harold Loomis (later revised by Shlomo Sternberg) that develops multivariable calculus and analysis with a strong emphasis on proofs and theoretical foundations.
-
A.
Functional Analysis: Introduction to Further Topics in Analysis
"Functional Analysis: Introduction to Further Topics in Analysis" is an advanced graduate-level textbook by Elias Stein that develops modern functional analysis with applications to areas such as operator theory, harmonic analysis, and partial differential equations.
-
B.
Master of Mathematics (M.Math.)
The Master of Mathematics (M.Math.) is a highly rigorous postgraduate program in advanced mathematics, known for its strong theoretical foundation and emphasis on research-oriented training.
-
C.
Mueller calculus
Mueller calculus is a mathematical framework in polarization optics that uses matrix operations to describe how optical elements transform the Stokes parameters of light.
-
D.
Calculus Made Easy
Calculus Made Easy is a classic introductory mathematics book that simplifies and demystifies the fundamental concepts of calculus for beginners.
-
E.
Principles of Mathematics
Principles of Mathematics is Bertrand Russell’s foundational work in mathematical logic and the philosophy of mathematics, arguing that mathematics can be derived from purely logical principles.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
analysis textbook
ⓘ
calculus textbook ⓘ mathematics textbook ⓘ university textbook ⓘ |
| contains | numerous challenging exercises ⓘ |
| coversTopic |
Banach spaces (introductory)
ⓘ
Fourier series ⓘ Green's theorem ⓘ Jacobian matrices ⓘ Stokes' theorem ⓘ change of variables formula ⓘ differential forms ⓘ differentiation in several variables ⓘ limits and continuity in several variables ⓘ line integrals ⓘ linear transformations ⓘ metric spaces ⓘ multiple integrals ⓘ sequences and series of functions ⓘ surface integrals ⓘ the divergence theorem ⓘ the implicit function theorem ⓘ the inverse function theorem ⓘ uniform convergence ⓘ |
| emphasis |
epsilon–delta definitions
ⓘ
mathematical rigor ⓘ rigorous proofs ⓘ theoretical foundations of calculus ⓘ |
| field |
analysis
ⓘ
calculus ⓘ mathematics ⓘ |
| hasAuthor | Lynn Harold Loomis ⓘ |
| hasContributor | Shlomo Sternberg ⓘ |
| hasReviser | Shlomo Sternberg ⓘ |
| language | English ⓘ |
| level |
introductory graduate
ⓘ
upper-level undergraduate ⓘ |
| pedagogicalStyle |
problem-oriented
ⓘ
theorem–proof format ⓘ |
| subject |
linear algebra (as used in analysis)
ⓘ
mathematical analysis ⓘ multivariable calculus ⓘ real analysis ⓘ vector calculus ⓘ |
| targetAudience |
beginning graduate students
ⓘ
upper-level undergraduates ⓘ |
| usedFor |
advanced calculus courses
ⓘ
honors calculus courses ⓘ introductory real analysis courses ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Advanced Calculus Description of subject: Advanced Calculus is a rigorous upper-level mathematics textbook by Lynn Harold Loomis (later revised by Shlomo Sternberg) that develops multivariable calculus and analysis with a strong emphasis on proofs and theoretical foundations.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.