Our Work

Julia Team
NKUA

Crafted for accessibility and engagement, our work is an effort to transform learning into an enjoyable and approachable journey.

We present a brief introduction & guide to Julia language. We examine calculation of pivot patterns emerging from application of GECP in Hadamard matrices, Benchmarks between Julia, Matlab & Python in applications of matrix computations & the Newton-Raphson method, Base conversion programs, Polynomial Interpolation, Natural Cubic Splines, Accuracy of different expressions of equal quantities.

Julia Guide

A description of Julia Language( History, Characteristics, Features, Environments, Tools, Frameworks, Specification of the Language etc.)

Guide
Interactive

Anastasia-Efterpi Psitou

Math Undergraduate

$Accuracy of fomrulae: (a+b)(a-b) or a^2-b^2$

Accuracy of fomrulae: (a+b)(a-b) or a^2-b^2

Calculates exact result of formulae (a+b)(a-b) & a^2-b^2 via the BigFloat datatype provided by Julia (a ≈ b), relative errors for each of the 2 methods and compares them.

Arithmetical Analysis

Nikolas Koukoudakis

Math Undergraduate

Prime Number Check Benchmarks

Benchmark between Julia, Matlab & Python for 3 algorithms that check if a number is prime or not. Namely: Bruteforce, Improved Bruteforce & Root Algorithm.

Number Theory
Interactive

Panagiotis Maniatakos

Math Undergraduate

Decimal to b-ary conversion

Mathematical background of decimal to b-ary integer & fractional conversion with the result being saves in 24-bit fixed point format.

Arithmetical Analysis
Computer Arithmetic
Interactive

Giannis Tsagkaropoulos

Math Undergraduate

Binary Saving Formats

Introduces decimal to binary conversion & the following saving formats: Fixed-point 24-bits, IEEE 754 32-bits, IEEE 754 64-bits

Arithmetical Analysis
Computer Arithmetic
Interactive

Giannis Tsagkaropoulos

Math Undergraduate

Binary Rationals

Given 2 decimal numbers, a & b, and a maximum length of the fractional part, the programm will produce all the numbers in [a,b] with a finite binary representation (binary rationals).

Arithmetical Analysis
Computer Arithmetic
Interactive

Giannis Tsagkaropoulos

Math Undergraduate

Benchmarks for Netwon-Raphson & Calculation of A’ · A · A’ product

Benchmark between Julia, Matlab & Python for Newton-Raphson method & for the calculation of the product: “ A’ · A · A’ ” (either from right to left or from left to right).

Arithmetical Analysis
Interactive

Markos Theocharis Kremmydas

Math Undergraduate

Pivot Pattern Finder for Hadamard Matrices of Order 20 using GECP

Code which is used to find possible pivot patterns of Hadamard matrices of order 20 using GECP. Note: In order to avoid rounding errors, the use of rational numbers was chosen for significant operations with potentially non-integer results.

Arithmetical Linear Algebra
Applied Mathematics

Emmanouil Lardas

Math Undergraduate

Interpolation Polynomials

Mathematical theory of Interpolation Polynomials & interactive interpolation of given functions with Lagrange's and Newton's interpolations methods.

Arithmetical Analysis
Intepolation
Interactive

Giannis Tsagkaropoulos

Math Undergraduate

Natural Cubic Spline

Brief introduction to natural cubic splines, algebra behind their construction & interactive interpolation of given functions using natural cubic splines.

Arithmetical Analysis
Interpolation
Interactive

Giannis Tsagkaropoulos

Math Undergraduate

A special thanks to Pluto.jl

The ultimate browser based notebook interface for the Julia language which allows presentation of Julia code & computational results in a tightly linked fashion.

Reactivity

Interactivity as a fundamental principle

A simple, reactive programming environment for Julia. Your programming environment becomes interactive by splitting your code into multiple cells!

Reproducibility

Pluto notebooks are reproducible by default

Pluto goes to great lengths to make sure that someone else will be able to run your notebook when you're done!

Education

A programming environment designed for learning and teaching

Crafted with the goal of creating a programming environment that is powerful, helpful and interactive, without being too intimidating for students and teachers.

The result?

A programming environment that prioritizes beginners over advanced users!