Lectures related to Computation: information representation

Polynomials: Operations and Properties

Explores polynomial operations, properties, and subspaces in vector spaces.

Vector Spaces: Definitions and Properties

Covers the definitions and properties of vector spaces, including axioms and examples.

Complex Numbers: Operations and Applications

Covers the properties and operations of complex numbers and their applications.

Modular Arithmetic: Operations and Polynomials

Covers modular arithmetic operations and polynomial calculations modulo N with various examples.

Vector Spaces: Properties and Operations

Covers the properties and operations of vector spaces, including addition and scalar multiplication.

Polynomials, Division, and Ideals

Explores polynomials, their operations, and the concept of ideals in polynomial rings.

Computer Arithmetic (Integers)

Covers binary representation, two's complement, overflow detection, and operations in MIPS for computer arithmetic with integers.

Algebraic Operations

Covers the basic concepts of rational numbers and algebraic operations, including addition, subtraction, multiplication, and division.

Subtraction: Properties and Definitions

Covers the properties and definitions of subtraction using addition and multiplication as a basis.

Vector Spaces: Definition, R2

Introduces vector spaces with binary addition and scalar multiplication, exploring geometric examples in R2.

Linear Combinations and Vector Spaces

Introduces linear combinations in vector spaces, operations, and polynomials of degree 2.

Vector Spaces: Definitions and Examples

Covers the definition and examples of vector spaces, including subspaces and linear transformations.

Geometry: Euclidean Elements & Vitruvius

Explores Euclid's first proposition, ancient symmetria, and Vitruvius' architectural figures.

Integer Representations: Magnitude & Complement

Explores integer representations, focusing on sign-and-magnitude, one's complement, two's complement, Excess-N, overflow, underflow, and binary multiplication.

Complex Numbers: Operations and Representations

Explores complex numbers, their operations, and representations in Cartesian and polar forms.

Element-Wise Operations

Covers element-wise operations in MATLAB and Octave using matrices and vectors.

Logic Systems: Representations and Arithmetic

Explores logic system representations, place-value notation, addition, subtraction, and digital system limitations, culminating in a multifunction alarm watch project.

Polynomial Applications: Combinatorial Computations

Delves into using polynomials for combinatorial computations and explores operations and identities with binomial coefficients.

Understanding Equivalence Relations and Integer Construction

Covers the construction of integers through equivalence relations and their properties in mathematics.

Elementary Operations in Geometry

Explores elementary operations in geometry, including addition, subtraction, multiplication, and division of segments and angles.