OCME · Bilingual mathematics & derivations
First Modern Structures: Oscillators, Discounting, Complex Numbers, Vector Spaces, Finite Groups, Metrics and Distributions
On this page
- Ordinary differential equation
- Differentiating polynomial sums, products, and compositions
- Natural-number powers and principal square roots
- Compound-interest model
- Fraction
- Equation
- Real number
- Coordinate plane
- Arithmetic operations
- Plane vectors in a fixed basis
- Set
- Function mapping
- Binary relations and set projections
- Mathematical proof
- Usual order on the real numbers
- Real random variables on finite sample spaces
- Probability on finite sample spaces
- Linear harmonic-oscillator model
- Present value and discounting
- Complex number
- Real vector space
- Finite group
- Metric space
- Finite discrete probability distribution
Complete seven traceable knowledge objects in dependency order on the existing number-system and function foundations.
This is a suggested learning sequence, not a universal logical dependency or a formal proof.
Ordinary differential equation
Existing canonical prerequisite for the new objects in this pulse.
Differentiating polynomial sums, products, and compositions
Existing canonical prerequisite for the new objects in this pulse.
Natural-number powers and principal square roots
Existing canonical prerequisite for the new objects in this pulse.
Compound-interest model
Existing canonical prerequisite for the new objects in this pulse.
Fraction
Existing canonical prerequisite for the new objects in this pulse.
Equation
Existing canonical prerequisite for the new objects in this pulse.
Real number
Existing canonical prerequisite for the new objects in this pulse.
Coordinate plane
Existing canonical prerequisite for the new objects in this pulse.
Arithmetic operations
Existing canonical prerequisite for the new objects in this pulse.
Plane vectors in a fixed basis
Existing canonical prerequisite for the new objects in this pulse.
Set
Existing canonical prerequisite for the new objects in this pulse.
Function mapping
Existing canonical prerequisite for the new objects in this pulse.
Binary relations and set projections
Existing canonical prerequisite for the new objects in this pulse.
Mathematical proof
Existing canonical prerequisite for the new objects in this pulse.
Usual order on the real numbers
Existing canonical prerequisite for the new objects in this pulse.
Real random variables on finite sample spaces
Existing canonical prerequisite for the new objects in this pulse.
Probability on finite sample spaces
Existing canonical prerequisite for the new objects in this pulse.
Linear harmonic-oscillator model
The undamped linear harmonic oscillator is defined by m*x″+k*x=0 with m,k>0; this slice asserts no trigonometric closed-form solution.
Present value and discounting
For a fixed positive accumulation factor and period count, divide a future amount by the factor power to obtain present value.
Complex number
A complex number a+b*i is represented by the ordered real pair (a,b), with addition, subtraction and multiplication defined using i²=−1.
Real vector space
A real vector space has vector addition and real scalar multiplication, satisfying the additive abelian-group and compatible scalar-action axioms.
Finite group
A finite group has a finite carrier and complete closed Cayley table, satisfying associativity, a unique identity and inverses for every element.
Metric space
A metric space has a carrier set and a distance function that is nonnegative, zero exactly at equal points, symmetric and satisfies the triangle inequality.
Finite discrete probability distribution
A finite discrete distribution assigns nonnegative probability masses to finitely many outcome values, with exact total mass one.
Path source & status
path-pulse-foundations-20261022 · candidate