Concrete Mathematics
E32450
Concrete Mathematics is a widely respected textbook by Ronald Graham, Donald Knuth, and Oren Patashnik that blends continuous and discrete mathematics with an emphasis on problem-solving and rigorous analysis, especially for computer science applications.
All labels observed (4)
| Label | Occurrences |
|---|---|
| Concrete Mathematics canonical | 4 |
| Concrete Mathematics: A Foundation for Computer Science | 2 |
| "Concrete Mathematics" | 1 |
| "Concrete Mathematics: A Foundation for Computer Science" | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T249041 — 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: Concrete Mathematics Context triple: [Addison-Wesley, hasPublished, Concrete Mathematics]
-
A.
Winning Ways for your Mathematical Plays
Winning Ways for your Mathematical Plays is a multi-volume book on combinatorial game theory that popularizes and systematically explores mathematical games and their underlying structures.
-
B.
Disquisitiones Arithmeticae
Disquisitiones Arithmeticae is a foundational 1801 treatise on number theory that systematically developed the subject and introduced many of its central concepts and methods.
-
C.
Dyson’s transform in number theory
Dyson’s transform in number theory is a combinatorial technique introduced by Freeman Dyson to manipulate and relate integer partitions, particularly in the study of partition identities and congruences.
-
D.
Surreal numbers
Surreal numbers are a class of numbers introduced by John H. Conway that form an extensive ordered field encompassing the real numbers, infinite quantities, and infinitesimals within a unified framework.
-
E.
On Numbers and Games
On Numbers and Games is a mathematical book by John H. Conway that introduces surreal numbers and explores combinatorial game theory in a rigorous yet playful style.
- 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: Concrete Mathematics Target entity description: Concrete Mathematics is a widely respected textbook by Ronald Graham, Donald Knuth, and Oren Patashnik that blends continuous and discrete mathematics with an emphasis on problem-solving and rigorous analysis, especially for computer science applications.
-
A.
Winning Ways for your Mathematical Plays
Winning Ways for your Mathematical Plays is a multi-volume book on combinatorial game theory that popularizes and systematically explores mathematical games and their underlying structures.
-
B.
Disquisitiones Arithmeticae
Disquisitiones Arithmeticae is a foundational 1801 treatise on number theory that systematically developed the subject and introduced many of its central concepts and methods.
-
C.
Dyson’s transform in number theory
Dyson’s transform in number theory is a combinatorial technique introduced by Freeman Dyson to manipulate and relate integer partitions, particularly in the study of partition identities and congruences.
-
D.
Surreal numbers
Surreal numbers are a class of numbers introduced by John H. Conway that form an extensive ordered field encompassing the real numbers, infinite quantities, and infinitesimals within a unified framework.
-
E.
On Numbers and Games
On Numbers and Games is a mathematical book by John H. Conway that introduces surreal numbers and explores combinatorial game theory in a rigorous yet playful style.
- F. None of above. chosen
Statements (49)
| Predicate | Object |
|---|---|
| instanceOf |
computer science textbook
ⓘ
mathematics book ⓘ textbook ⓘ |
| author |
Donald E. Knuth
ⓘ
Oren Patashnik ⓘ Ronald L. Graham ⓘ |
| edition |
first edition
ⓘ
second edition ⓘ |
| emphasis |
problem solving
ⓘ
rigorous analysis ⓘ techniques for computer science ⓘ |
| field |
computer science
ⓘ
mathematics ⓘ |
| firstEditionPublicationYear | 1989 ⓘ |
| fullTitle |
Concrete Mathematics
self-linksurface differs
ⓘ
surface form:
Concrete Mathematics: A Foundation for Computer Science
|
| hasAbbreviation | CM ⓘ |
| hasExerciseFeatures |
detailed solutions to selected problems
ⓘ
problems of varying difficulty ⓘ |
| hasTheme | "concrete" as a blend of continuous and discrete ⓘ |
| influencedField |
analysis of algorithms
ⓘ
theoretical computer science education ⓘ |
| isWidelyUsedAs | reference for combinatorial and discrete techniques ⓘ |
| language | English ⓘ |
| notableFor |
blending continuous and discrete mathematics
ⓘ
influence on algorithm analysis ⓘ large collection of challenging exercises ⓘ |
| pedagogicalStyle |
emphasis on worked examples
ⓘ
informal but rigorous exposition ⓘ |
| publisher | Addison-Wesley ⓘ |
| relatedWork | The Art of Computer Programming ⓘ |
| secondEditionPublicationYear | 1994 ⓘ |
| subject |
asymptotic analysis
ⓘ
binomial coefficients ⓘ combinatorics ⓘ continuous mathematics ⓘ discrete mathematics ⓘ discrete probability ⓘ generating functions ⓘ number theory ⓘ recurrence relations ⓘ special numbers and polynomials ⓘ summation techniques ⓘ |
| targetAudience |
advanced undergraduates
ⓘ
graduate students ⓘ mathematically inclined programmers ⓘ researchers in computer science ⓘ |
| typicalCourseLevel |
graduate level
ⓘ
upper-division undergraduate ⓘ |
| usesNotation |
Knuth’s up-arrow notation
ⓘ
surface form:
Knuth up-arrow notation
|
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: Concrete Mathematics Description of subject: Concrete Mathematics is a widely respected textbook by Ronald Graham, Donald Knuth, and Oren Patashnik that blends continuous and discrete mathematics with an emphasis on problem-solving and rigorous analysis, especially for computer science applications.
Referenced by (8)
Full triples — surface form annotated when it differs from this entity's canonical label.
this entity surface form:
Concrete Mathematics: A Foundation for Computer Science
this entity surface form:
"Concrete Mathematics"
this entity surface form:
"Concrete Mathematics: A Foundation for Computer Science"
this entity surface form:
Concrete Mathematics: A Foundation for Computer Science