Math I: Calculus¶
Year 1 · Block 1a · Mathematics
Build from sets, numbers and limits to differentiation, series and integration.
- 12 lectures
- 138 concept pages
Practise¶
Lectures¶
1Sets and arithmetic17 concepts
- Set
- Singleton Set
- Subset
- Union of Sets
- Difference Set
- Empty Set
- Intersection of Sets
- Natural Number
- Proper Subset
- Addition and Sum
- Complement
- Disjoint Sets
- Finite and Infinite Sets
- Mathematical Induction
- Multiplication and Product
- Exponentiation and Power
- Factorial
Review lecture 1 in Concept Finder 17 concepts
2Real numbers and inequalities17 concepts
- Exponentiation and Power
- Infinity
- Integer
- Negation
- Rational Number
- Real Number
- Reciprocal
- Sequence
- Subtraction and Difference
- Trichotomy of Real Numbers
- Absolute Value
- Division and Quotient
- Finite Sequence
- Inequality
- Irrational Number
- Triangle Inequality
- Bounded Sequence
Review lecture 2 in Concept Finder 17 concepts
3Bounds, suprema and limits of sequences17 concepts
- Bounded Sequence
- Exponentiation and Power
- Extended Real Number
- Limit of a Sequence
- Lower Bound
- Maximum of a Set
- Minimum of a Set
- Monotone Sequence
- Squeeze Theorem for Sequences
- Subsequence
- Upper Bound
- Euler's Number
- Infimum
- Limit Laws for Sequences
- Supremum
- Monotone Convergence Theorem
- n-th Root
Review lecture 3 in Concept Finder 17 concepts
4Functions28 concepts
- Cartesian Coordinate System
- Exponentiation and Power
- Function
- Graph of a Function
- Identity Function
- Indicator Function
- Interval
- Monomial and Power Function
- Monotone Function
- n-th Root
- Polynomial
- Range and Image
- Rational Function
- Trigonometric Functions
- Zero of a Function
- Bounded Function
- Codomain
- Constant Function
- Dirichlet Function
- Domain
- Endpoint and Bounded Interval
- Exponential Function
- Injective Function
- Surjective Function
- Bijection and Inverse Function
- Bounded Set
- Composition of Functions
- Logarithm and Logarithmic Function
Review lecture 4 in Concept Finder 28 concepts
5Limits and continuity of functions17 concepts
- Floor and Ceiling Functions
- Global Extremum
- Limit at Infinity
- Punctured Neighbourhood
- Signum Function
- Horizontal Asymptote
- Limit at a Point
- Limit Laws for Functions
- One-Sided Limit
- Squeeze Theorem for Functions
- Continuity
- Divergence to Infinity
- Extreme Value Theorem
- Intermediate Value Theorem
- One-Sided Continuity
- Singularity
- Vertical Asymptote
Review lecture 5 in Concept Finder 17 concepts
6Derivatives and critical points9 concepts
- Derivative and Differentiability
- Differential
- Differentiation Rules
- Local Extremum
- One-Sided Derivative
- Stationary Point
- Chain Rule
- Critical Point
- First-Order Condition
Review lecture 6 in Concept Finder 9 concepts
7Mean value theorem and inverse functions5 concepts
- Inverse Function Theorem
- Inverse Trigonometric Functions
- Mean Value Theorem
- Monotone Function
- Rolle’s Theorem
Review lecture 7 in Concept Finder 5 concepts
8L'Hôpital's rule and indeterminate forms3 concepts
Review lecture 8 in Concept Finder 3 concepts
9Higher derivatives and convexity5 concepts
- Convexity and Concavity
- Higher Order Derivative
- Inflection Point
- Second-Order Condition
- Differentiability Class
Review lecture 9 in Concept Finder 5 concepts
10Series and Riemann sums12 concepts
- Finite Series
- Infinite Series
- Length of an Interval
- Partition of an Interval
- Riemann Sum
- Alternating Series
- Alternating Series Test
- Arithmetic Series
- Comparison Test for Series
- Geometric Series
- Harmonic Series
- Riemann Integral
Review lecture 10 in Concept Finder 12 concepts
11Integrals and the fundamental theorem6 concepts
- Antiderivative
- Definite Integral
- Fundamental Theorem of Calculus Part 1
- Fundamental Theorem of Calculus Part 2
- Indefinite Integral
- Integrand
Review lecture 11 in Concept Finder 6 concepts
12Integration techniques and improper integrals9 concepts
- Improper Integral
- Integral Test for Convergence
- Integration by Parts
- Integration by Substitution Type 1
- Integration by Substitution Type 2
- -test
- Singularity
- Comparison Test for Improper Integrals
- p-series
Review lecture 12 in Concept Finder 9 concepts
Concepts appear in the lecture that introduces them, foundations first. Lecture titles summarise the concepts tagged to each lecture; a course name after a concept marks a page from another course used that lecture.
FoundationsSets, numbers, arithmetic, bounds, and sequences.48 concepts
Sets 11
Number systems 9
Arithmetic and inequalities 12
Intervals and bounds 10
FunctionsFunction language, properties, and the standard functions.27 concepts
Function language 13
Standard functions 14
- Constant Function
- Identity Function
- Monomial and Power Function
- Polynomial
- Rational Function
- Euler's Number
- Exponential Function
- Logarithm and Logarithmic Function
- Trigonometric Functions
- Inverse Trigonometric Functions
- Signum Function
- Floor and Ceiling Functions
- Indicator Function
- Dirichlet Function
Limits and continuityDefinitions, tools, and core theorems.18 concepts
Limits 9
Limit tools 4
Continuity 3
Continuity theorems 2
DifferentiationRules, approximation, extrema, and key theorems.20 concepts
Essentials 6
Extrema and shape 8
Approximation 2
SeriesSeries and convergence tests.10 concepts
Core series 7
Convergence tests 3
IntegrationRiemann machinery, FTC, and standard techniques.15 concepts
FTC and techniques 5
Riemann machinery 3
Improper integrals and tests 3
More about this course¶
Where it leadsLater courses on the wiki that build on these concepts.10 courses
- Function
- Subset
- Union of Sets
- Continuity
- Infinite Series
- Limit of a Sequence
-
+25 moreShow fewer
- Polynomial
- Intersection of Sets
- Interval
- Monomial and Power Function
- Supremum
- Triangle Inequality
- Bounded Function
- Codomain
- Disjoint Sets
- Domain
- Empty Set
- Exponentiation and Power
- Extended Real Number
- Finite and Infinite Sets
- Higher-Order Derivative
- Infimum
- Limit at a Point
- Limit at Infinity
- Maximum of a Set
- Minimum of a Set
- n-th Root
- Singleton Set
- Subsequence
- Trigonometric Functions
- Upper Bound
- Set
- Exponential Function
- Definite Integral
- Function
- Intersection of Sets
- Factorial
-
+16 moreShow fewer
Also: Math V: Advanced Linear Algebra (via Exponential Function), Probability Distributions (via Limit of a Sequence), Life Insurance (via Geometric Series), Game Theory (via Function), Risk Insurance (via Convexity and Concavity), OR Modelling (via Cartesian Coordinate System)
AchievementsCourse challenges and how many learners hold them
Further readingEnrichment pages for self-study, outside the core course2
These enrichment pages are available for self-study and are kept separate from the core learning pool.
For teachers and tutorsPrepare the connections for your next explanation
Choose a concept for your next explanation. Review its recorded foundations and later uses, then check the concept page's sources against your own course material.
The workbench uses published prerequisite links. It describes concept relationships; class performance and teaching coverage need separate evidence.
Aliases: M1, Math 1
Last updated: 26 October 2026 00:09