Higher mathematics is a vast landscape of abstract structures, logical proofs, and complex problem-solving

by James Munkres. A standard reference known for its clarity and high-quality printing, making it a reliable reference for years. Linear Algebra: Linear Algebra Done Right

  • Conceptual: Linear Algebra Done Right — Sheldon Axler.
  • Applied + theory: Matrix Analysis — Horn & Johnson (advanced).

"Understanding Analysis" by Stephen Abbott: If Rudin feels like a brick wall, Abbott is the ladder. It is exceptionally well-written, focusing on the "why" and the beauty of the subject rather than just the technical grind. 3. Abstract Algebra: The Study of Structure

  • Differential Geometry:
  • "Visual Complex Analysis" by Tristan Needham

    Number Theory (The logic of integers)

    • "A Classical Introduction to Modern Number Theory" by Kenneth Ireland and Michael Rosen

      Here is a curated roadmap of the foundational and advanced texts that have shaped the minds of mathematicians for decades. 1. The Gateway: Transition to Higher Math

      The transition from computational mathematics (Calculus, Linear Algebra) to proof-based "higher" mathematics (Abstract Algebra, Topology, Real Analysis) is one of the most challenging hurdles a student faces. It requires a shift in mindset from "finding the answer" to "proving the truth."

  • A world of geom

    ggplot2 builds charts through layers using geom_ functions. Here is a list of the different available geoms. Click one to see an example using it.

    geom_bar geom_bin geom_boxplot geom_density geom_error geom_hex geom_hist geom_hline geom_jitter geom_label geom_line geom_point geom_polygon geom_rect geom_ribbon geom_rug geom_segment geom_smooth geom_text geom_tile geom_violin geom_vline
    Annotation with ggplot2

    Annotation is a key step in data visualization. It allows to highlight the main message of the chart, turning a messy figure in an insightful medium. ggplot2 offers many function for this purpose, allowing to add all sorts of text and shapes.





    Marginal plot

    Marginal plots are not natively supported by ggplot2, but their realisation is straightforward thanks to the ggExtra library as illustrated in graph #277.





    ggplot2 chart appearance

    The theme() function of ggplot2 allows to customize the chart appearance. It controls 3 main types of components:

    • Axis: controls the title, label, line and ticks
    • Background: controls the background color and the major and minor grid lines
    • Legend: controls position, text, symbols and more.
    Re-ordering with ggplot2


    When working with categorical variables (= factors), a common struggle is to manage the order of entities on the plot.

    Post #267 is dedicated to reordering. It describes 3 different way to arrange groups in a ggplot2 chart:


    Read post
    Tidyverse

    Here’s the official ggplot2 cheatsheet created by Posit. It covers all the key concepts of the library.

    I've also compiled it with the most useful R and data visualization cheatsheets into a single PDF you can download:

    ggplot2 title

    The ggtitle() function allows to add a title to the chart. The following post will guide you through its usage, showing how to control title main features: position, font, color, text and more.





    Use custom fonts with ggplot2

    If you don't want your plot to look like any others, you'll definitely be interested in using custom fonts for your title and labels! This is totally possible thanks to 2 main packages: ragg and showtext. The blog-post below should help you using any font in minutes.





    Small multiples: facet_wrap() and facet_grid()

    Small multiples is a very powerful dataviz technique. It split the chart window in many small similar charts: each represents a specific group of a categorical variable. The following post describes the main use cases using facet_wrap() and facet_grid() and should get you started quickly.

    A set of pre-built themes

    It is possible to customize any part of a ggplot2 chart thanks to the theme() function. Fortunately, heaps of pre-built themes are available, allowing to get a good style with one more line of code only. Here is a glimpse of the available themes. See code

    Higher Mathematics Books -

    Higher mathematics is a vast landscape of abstract structures, logical proofs, and complex problem-solving

    by James Munkres. A standard reference known for its clarity and high-quality printing, making it a reliable reference for years. Linear Algebra: Linear Algebra Done Right

    • Conceptual: Linear Algebra Done Right — Sheldon Axler.
    • Applied + theory: Matrix Analysis — Horn & Johnson (advanced).

    "Understanding Analysis" by Stephen Abbott: If Rudin feels like a brick wall, Abbott is the ladder. It is exceptionally well-written, focusing on the "why" and the beauty of the subject rather than just the technical grind. 3. Abstract Algebra: The Study of Structure

  • Differential Geometry:
  • "Visual Complex Analysis" by Tristan Needham

    Number Theory (The logic of integers)

    • "A Classical Introduction to Modern Number Theory" by Kenneth Ireland and Michael Rosen

      Here is a curated roadmap of the foundational and advanced texts that have shaped the minds of mathematicians for decades. 1. The Gateway: Transition to Higher Math

      The transition from computational mathematics (Calculus, Linear Algebra) to proof-based "higher" mathematics (Abstract Algebra, Topology, Real Analysis) is one of the most challenging hurdles a student faces. It requires a shift in mindset from "finding the answer" to "proving the truth."

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