Learning & Notebook / Study area
Mathematics
Study record being developedI study mathematics to reason clearly, understand relationships, and solve problems. This section will collect my notes, worked examples, and applications as I develop my understanding.
Mathematics study outline
This is a condensed topic guide drawn from textbooks and university courses. It is not a verbatim textbook contents list or a record of completed courses. Subjects overlap, and later study branches into separate areas.
Each subject can collect notes, worked problems, corrections, and practical applications as my study develops.
Foundations through precalculus
1. Arithmetic
- Whole-number operations
- factors and multiples
- fractions
- decimals
- percentages
- ratios and proportions
- measurement
- basic geometry
Source outline
2. Pre-algebra
- Variables and expressions
- order of operations
- signed numbers
- number properties
- simple equations
- applications
- introductory graphing
Source outline
3. Elementary algebra
- Linear equations and inequalities
- word problems
- coordinate graphs
- systems
- exponents
- polynomials
- factoring
- rational expressions
- radicals
- quadratics
Source outline
4. Intermediate algebra
- Functions and graphs
- equations and inequalities
- systems
- polynomial and rational functions
- radicals
- complex numbers
- quadratics
- exponentials and logarithms
- conic sections
Source outline
5. College algebra
- Algebra review
- equations and inequalities
- function notation and transformations
- linear models
- polynomial and rational functions
- exponentials and logarithms
- systems and matrices
- sequences
Source outline
6. Trigonometry
- Angles
- right triangles
- unit circle
- trigonometric graphs
- inverse functions
- identities
- equations
- laws of sines and cosines
- vectors
- polar coordinates
Source outline
7. Precalculus
- Functions and models
- exponentials and logarithms
- trigonometry
- identities
- vectors
- parametric equations
- systems
- conic sections
- sequences
- introductory limits
Source outline
Calculus sequence
8. Calculus I
- Functions
- limits and continuity
- derivatives and rules
- implicit differentiation
- related rates
- optimization
- antiderivatives
- definite integrals
- fundamental theorem of calculus
Source outline
9. Calculus II
- Integration methods
- area, volume and length
- improper integrals
- introductory differential equations
- sequences
- convergence
- power and Taylor series
- parametric and polar curves
Source outline
10. Calculus III
- Vectors and three-dimensional geometry
- vector-valued functions
- partial derivatives
- gradients
- optimization
- multiple integrals
- coordinate transformations
- vector fields
- line and surface integrals
- vector-calculus theorems
Source outline
Further mathematics
11. Linear algebra
- Systems
- elimination
- matrices
- vector spaces
- independence
- basis and dimension
- transformations
- orthogonality
- least squares
- determinants
- eigenvalues
- diagonalization
- singular value decomposition
Source outline
12. Differential equations
- First-order equations
- models
- higher-order equations
- systems
- qualitative behavior
- Laplace transforms
- series methods
- Fourier series
- introductory partial differential equations
Source outline
13. Discrete mathematics
- Logic
- sets and relations
- proofs
- induction
- counting
- graphs
- recurrences
- algorithm growth
- number theory
- discrete probability
Source outline
14. Mathematical proofs
- Statements and quantifiers
- direct arguments
- contrapositive
- contradiction
- induction
- sets
- functions
- relations
- counterexamples
Source outline
Statistics and applied branches
15. Introductory statistics
- Data collection
- descriptive measures
- probability
- distributions
- normal models
- sampling
- central limit theorem
- confidence intervals
- hypothesis tests
- regression
- chi-square methods
- analysis of variance
Source outline
16. Probability
- Counting
- sample spaces
- conditional probability
- independence
- Bayes’ theorem
- random variables
- distributions
- expected values
- variance
- joint distributions
- limit theorems
Source outline
17. Finite mathematics
- Linear systems and matrices
- financial mathematics
- linear programming
- counting
- probability
- decision models
Proposed topic grouping. A specific textbook has not yet been selected.
18. Business calculus
- Functions and business models
- limits
- derivatives
- marginal analysis
- optimization
- exponential growth
- integration
- accumulated change
Proposed topic grouping. A specific textbook has not yet been selected.
Advanced study
19. Real analysis
- Real-number properties
- sequences and series
- continuity
- differentiation
- integration
- convergence of functions
- metric spaces
Source outline
20. Abstract algebra
- Integers
- modular arithmetic
- groups
- subgroups
- permutations
- cosets
- homomorphisms
- quotient structures
- rings
- polynomials
- fields
- introductory Galois theory
Source outline
21. Topology
- Topological spaces
- continuity
- subspaces
- products and quotients
- connectedness
- compactness
- separation properties
- metric-space connections
- introductory fundamental groups
Source outline
22. Numerical analysis
- Numerical error
- root-finding
- interpolation
- approximation
- numerical differentiation and integration
- matrix computations
- numerical differential equations
Source outline
Worked problems
Each entry will state the problem, explain the method, show the steps, and check the answer. Corrections and alternative approaches will remain part of the learning record.
Practical applications
I plan to connect mathematics to expense analysis, performance measures, scientific calculations, and future technical projects.
Study record
No worked problems have been published here yet. The next step is to choose a topic and add a first example with a clear explanation.
