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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

Julia Guide

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

  • Guide
  • Interactive

Anastasia-Efterpi Psitou

B.Sc. in Mathematics*

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

B.Sc. in Mathematics*

Prime Number Check Benchmarks

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

B.Sc. in Mathematics*

Decimal to b-ary conversion

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

B.Sc. in Mathematics*

Binary Saving Formats

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

B.Sc. in Mathematics*

Binary Rationals

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

B.Sc. in Mathematics*

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

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

B.Sc. in Mathematics*

Pivot Pattern Finder for Hadamard Matrices of Order 20 using GECP

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

B.Sc. in Mathematics*

Interpolation Polynomials

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

B.Sc. in Mathematics*

Natural Cubic Spline

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

B.Sc. in Mathematics*

*Note: This is the educational status of creators of the notebooks, during the time of creation.

A special thanks to Pluto.jl

The ultimate browser-based notebook interface for the Julia language, tightly linking code and computational results.

Reactivity

Interactivity as a principle

A reactive environment where splitting code into cells makes your workflow instantly interactive.

Reproducibility

Reproducible by default

Pluto ensures that your work stays runnable for others, taking the guesswork out of environment management.

Education

Designed for Learning

Powerful and helpful without being intimidating for students.

Prioritizing beginners over experts.
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