Skip to content
  • support@n23d.com
  • 775-378-7945
  • Reno, NV
Admin Sales Support
N23D Engineering Group

N23D Engineering Group

Into 3D Modeling, Printing, Animation and Simulation

  • Home
  • Products
    • NFT
    • 3D Prints
  • Services
    • 3D Scanning – BIM
    • 3D Scanning – Mechanical
  • Contact Us
    • Sales
    • Support
    • Investors
  • Store
  • Toggle search form
  • Humanity, Physics, and Chemistry N23D
  • Specializations in Science – An Overview Science
  • Specializations in High Energy Physics High Energy Physics
  • Specializations in Structural Engineering Engineering
  • The Importance of Liberty and Honesty in AI Systems Artificial Intelligence
  • Pondering on the Meaning of Life Off Topic
  • Things to Know When Getting Started with 3D Printing 3D Printing
  • Things to Know When Getting Started with 3D Scanning 3D Scanning

Specializations in Formal Science

Posted on March 5, 2023March 5, 2023 By Bryan Riley No Comments on Specializations in Formal Science

Formal science is a branch of knowledge concerned with the study of abstract systems, such as mathematics, logic, and computer science. There are several specializations in formal science, including:

  1. Mathematics: This is the study of numbers, quantities, and shapes. It includes a wide range of subfields, such as algebra, geometry, calculus, and statistics.
  2. Logic: This is the study of reasoning and argumentation. It includes propositional logic, predicate logic, modal logic, and many other branches.
  3. Computer Science: This is the study of computation, programming, and algorithms. It includes subfields such as artificial intelligence, computer architecture, software engineering, and databases.
  4. Theoretical Computer Science: This is a subfield of computer science that focuses on the study of algorithms and computational complexity.
  5. Set Theory: This is the study of sets and their properties. It is a foundational field in mathematics and has important applications in logic and computer science.
  6. Category Theory: This is a branch of mathematics that studies the structure of mathematical objects and their relationships. It has applications in many areas of mathematics and theoretical computer science.
  7. Information Theory: This is the study of the quantification, storage, and communication of information. It has applications in communication systems, cryptography, and data compression.


Mathematics is a vast field with numerous specializations. Some of the most common specializations in mathematics include:

  1. Algebra: The study of abstract structures such as groups, rings, and fields.
  2. Analysis: The study of limits, continuity, differentiation, integration, and infinite series.
  3. Geometry: The study of shape, size, relative position of figures, and the properties of space.
  4. Topology: The study of the properties of spaces that are preserved under continuous transformations, such as stretching and bending.
  5. Number theory: The study of the properties of numbers, including prime numbers, integer solutions to equations, and properties of number systems.
  6. Combinatorics: The study of discrete structures and their relationships, including counting and graph theory.
  7. Probability theory: The study of randomness and uncertainty, including the analysis of random events and stochastic processes.
  8. Differential equations: The study of equations that describe how a system changes over time, including partial differential equations and ordinary differential equations.
  9. Applied mathematics: The application of mathematical methods to solve practical problems, including physics, engineering, economics, and social sciences.
  10. Mathematical logic: The study of mathematical reasoning and the foundations of mathematics, including formal systems, set theory, and model theory.

These are just a few of the many specializations within mathematics. There is a great deal of overlap between these fields, and many mathematicians work across multiple areas.



Logic is a broad field that encompasses a variety of subfields and specializations. Some of the most common specializations in logic include:

  1. Propositional logic: The study of the logical relationships between propositions or statements.
  2. Predicate logic: The study of the logical relationships between objects and their properties or attributes.
  3. Modal logic: The study of the logical relationships between propositions and the various modes of truth, such as necessity, possibility, and contingency.
  4. Non-classical logics: The study of alternative systems of logic that depart from the classical principles of truth and validity, such as fuzzy logic, paraconsistent logic, and intuitionistic logic.
  5. Model theory: The study of the relationship between formal languages and the mathematical structures that they represent.
  6. Proof theory: The study of the formal rules of inference and deduction in logical systems.
  7. Computability theory: The study of the limits of what can be computed by machines or algorithms.
  8. Set theory: The study of sets and their properties, including the foundations of mathematics.
  9. Philosophy of logic: The study of the nature and foundations of logical systems, as well as their role in philosophy, mathematics, and computer science.

These are just a few examples of the many specializations within logic. Logic is an interdisciplinary field, and many logicians work across multiple areas, including mathematics, philosophy, and computer science.



Computer science is a rapidly growing and diverse field with a variety of specializations. Some of the most common specializations in computer science include:

  1. Artificial intelligence (AI): The study of intelligent agents, which can be hardware or software that can perceive their environment and take actions to maximize their chances of success.
  2. Computer architecture: The study of the design and organization of computer systems, including the hardware and software components that make up these systems.
  3. Computer graphics: The study of creating and manipulating visual and multimedia content, including images, video, and animations.
  4. Computer networks: The study of the design, implementation, and management of computer communication networks, including local area networks (LANs), wide area networks (WANs), and the internet.
  5. Computer security: The study of protecting computer systems and networks from unauthorized access, damage, or theft.
  6. Database systems: The study of the design and management of databases, which are collections of data organized in a structured way.
  7. Human-computer interaction (HCI): The study of the interaction between humans and computers, with a focus on designing user interfaces that are intuitive, easy to use, and effective.
  8. Programming languages: The study of the design and implementation of programming languages, including their syntax, semantics, and pragmatics.
  9. Software engineering: The study of the design, development, and testing of software, including processes and methodologies for building high-quality software.
  10. Theory of computation: The study of fundamental principles underlying computation, including complexity theory, algorithms, and data structures.

These are just a few examples of the many specializations within computer science. Computer scientists often work across multiple areas, and many of these areas overlap with other fields, such as mathematics, engineering, and cognitive science.



Set theory is a branch of mathematical logic that deals with the study of sets and their properties. Some of the most common specializations within set theory include:

  1. Axiomatic set theory: The study of the foundations of set theory, including the development of formal axiomatic systems for set theory, such as Zermelo-Fraenkel set theory and its variants.
  2. Model theory of set theory: The study of the relationship between formal set-theoretic languages and the mathematical structures they represent, including models of set theory and the study of set-theoretic independence.
  3. Large cardinals: The study of the properties and consistency strength of large cardinal axioms, which assert the existence of sets with certain large cardinalities.
  4. Inner model theory: The study of the structure of inner models of set theory, which are sub-universes of the set-theoretic universe satisfying certain properties.
  5. Forcing: The study of the technique of forcing, which is used to prove independence results in set theory by constructing new models of set theory from old ones.
  6. Descriptive set theory: The study of the properties of sets that can be defined in terms of simpler sets using a finite number of logical operations.
  7. Category theory and set theory: The study of the relationship between category theory, which is a branch of mathematics concerned with the study of mathematical structures and their relationships, and set theory.

These are just a few examples of the many specializations within set theory. Set theory is a foundational area of mathematics, and many other areas of mathematics, as well as computer science, philosophy, and other fields, rely heavily on its concepts and techniques.



Category theory is a branch of mathematics that deals with the study of abstract mathematical structures and their relationships. Some of the most common specializations within category theory include:

  1. Topos theory: The study of topoi, which are generalizations of the notion of a space in topology. Topoi can be used to formalize many mathematical concepts, such as sheaf theory and algebraic geometry.
  2. Homotopy theory: The study of the homotopy groups of spaces and the maps between them. Homotopy theory is used in topology and algebraic geometry, as well as in the study of mathematical physics.
  3. Algebraic geometry: The study of geometric objects defined by algebraic equations. Category theory provides a powerful language and toolset for the study of algebraic geometry.
  4. Category-theoretic foundations of mathematics: The use of category theory as a foundational framework for mathematics, which allows for the development of theories that are independent of set-theoretic foundations.
  5. Categorical logic: The study of the relationship between logic and category theory, including the development of categorical versions of logic and the study of categorical models of logic.
  6. Higher category theory: The study of categories of categories, and their relationship to higher-dimensional structures such as n-categories and homotopy n-types.
  7. Quantum algebra and category theory: The study of the relationship between category theory and quantum mechanics, including the development of categorical models of quantum mechanics.

These are just a few examples of the many specializations within category theory. Category theory is a highly abstract and general field, and its concepts and techniques have found applications in many areas of mathematics, physics, computer science, and other fields.



Information theory is a branch of applied mathematics and electrical engineering that deals with the quantification, storage, and communication of information. Some of the most common specializations within information theory include:

  1. Coding theory: The study of the design and analysis of error-correcting codes, which are used to ensure reliable transmission of information over noisy channels.
  2. Data compression: The study of algorithms for compressing data, which can reduce the amount of storage or transmission bandwidth required for the data.
  3. Cryptography: The study of methods for secure communication and data storage, including encryption and digital signatures.
  4. Shannon theory: The study of the fundamental limits of information transmission and compression, as well as the concept of entropy as a measure of information.
  5. Network information theory: The study of information transmission and compression in communication networks, including the capacity of networks and the design of network codes.
  6. Quantum information theory: The study of the transmission and processing of quantum information, including the development of quantum error-correcting codes and quantum cryptography.
  7. Information theory and statistics: The study of the relationship between information theory and statistics, including the application of information-theoretic concepts to statistical inference.
  8. Information theory and machine learning: The study of the relationship between information theory and machine learning, including the use of information-theoretic measures to quantify the performance of machine learning algorithms.

These are just a few examples of the many specializations within information theory. Information theory has important applications in many fields, including communications, data storage, cryptography, machine learning, and signal processing.

Share this:

  • Tweet
Formal Science, Science

Post navigation

Previous Post: Specializations in Social Science
Next Post: Specializations in Astrophysics

Related Posts

  • Specializations in Optics Natural Science
  • Specializations in Condensed Matter Physics Condensed Matter Physics
  • Specializations in High Energy Physics High Energy Physics
  • Specializations in Natural Science Natural Science
  • Specializations in Astrophysics Natural Science
  • Specializations in Social Science Science

Leave a ReplyCancel reply

RSS Solidworks

  • SOLIDWORKS 2024 and the SOLIDWORKS Enhancement Ideas Community
  • MODSIM Webinar Series: Session 5 – Part 1: Innovating Super Cool & Connected High Tech Device Designs
  • Top Ten Enhancements in Collaborative Designer for SOLIDWORKS in 2023
  • Xi Engineering Leverages SOLIDWORKS to Speed Development and Win the Race to Market
  • Behlen Streamlines its Production Facility Virtually with Factory Simulation Engineer

RSS 3DPrint.com

  • Venture Formed to Develop Distributed 3D Printing Network in UAE
  • Custom 3D Printed Surgical Tools Pushed Forward via restor3d and Formlabs Partnership
  • On the Ground at AM Conclave: The UAE’s New 3D Printing Conference
  • Divergent 3D, Pelagus 3D, and More at the 2023 NAMIC Global AM Summit
  • Aussie RVs Receive 3D Printing Boost from $1.16M Government Grant

RSS Reason.com

  • California State Guidelines Discourage Schools From Offering Advanced Middle School Math 
  • Brickbat: Still Waiting
  • Defenders of the Florida and Texas Social Media Laws Contradict Themselves
  • Solicitation of Crime and "Things of Value" (Plus a Mother-of-the-Year Candidate)
  • Can a Marylander be the Senator from California?

RSS 3Ders

  • Campden BRI launches research project to evaluate how 3D printing could benefit food industry
  • 3D printed molds help to insulate NASA supersize Space Launch System
  • BMBF project IDAM to enable metallic 3D printing in automotive series production
  • Poietis granted third European patent for laser-assisted 3D bioprinting technology
  • GE Research uses 3D printing to design Ultra Performance Heat Exchanger

RSS Cartoon Brew

  • Walt Disney Pictures VFX Workers Unanimously Vote To Unionize With IATSE
  • Chinese Streamer Bilibili Unveils 68-Title Animation Pipeline As Demand For Local Productions Skyrockets
  • 2024 Oscars Short Film Contenders: ‘Rosemary A.D. (After Dad)’ Director Ethan Barrett
  • View Conference 2023 Takes Flight With Italian Premieres Of ‘Migration,’ ‘Chicken Run: Dawn Of The Nugget’
  • IATSE Working With DNEG Employees To Unionize Canadian Studios

RSS 3D Printing Industry

  • Desktop Metal cleared of fraud and stock manipulation after defeating investor lawsuit 
  • DEVELOP3D Live: Computational Design insights from nTop, LatticeRobot, Hyperganic Group, Additive Flow, and the Manufacturing Technology Centre
  • AMCM developing new 8-laser M 8K metal 3D printer for space rocket production
  • INTERVIEW: Thomas Batigne, Silicone 3D Printing with Lynxter
  • Zeda Inc. CTO, Greg Morris selected for the AMUG 2024 Innovators Award

RSS Animation World Network

  • Magic Frame Animation and Creation Entertainment Media's ‘Rebellious’ Gets Global Premiere
  • MPC Shares ‘Transformers: Rise of the Beasts’ VFX Breakdown Reel
  • Walt Disney Pictures VFX Workers Unanimously Vote to Unionize
  • Jellyfish Originals Adapting ‘Toto the Ninja Cat’
  • Charades Sells Key Territories for Annecy Winner ‘Chicken for Linda!’

RSS TechCrunch

  • Open Banking led to a FinTech boom — As Brite raises $60M, account-to-account payment grows
  • Indian fintech unicorn Slice secures rare approval to merge with bank
  • Krafton India launches gaming incubator to expand local ecosystem
  • Electric Hydrogen is the green hydrogen industry’s first unicorn
  • In latest Cruise incident, video shows pedestrian struck by human-driven car, then run over by robotaxi

RSS The Verge

  • Nintendo’s Wii U and 3DS online services will shut down in April
  • Samsung’s new ‘fan editions’ of the Galaxy S23, Tab S9, and Buds bring flagship features to lower prices
  • Verizon bundles Netflix and NFL Plus Premium for $25/month
  • The entire story of Twitter / X under Elon Musk
  • X has to pay $1.1 million in legal fees for ex-Twitter execs

RSS Animation Magazine

  • MIPJunior & MIPCOM: New Toons from Sony Kids, Blue Ant, MIAM! & Monster, Plus More ‘Fireman Sam’ & ‘Polly Pocket’
  • Michelle Grady Promoted to President of Sony Pictures Imageworks
  • ‘Spirited Away: Live on Stage’ Makes Digital & Blu-Ray Debut
  • ‘Captain Laserhawk’ Creator Adi Shankar Reveals the Inspirations Behind Netflix & Ubisoft’s Synthwave Hero
  • David H. Brooks Takes Us Behind the Scenes of His Spooktacular ‘Mickey and Friends Trick or Treats’ Special

RSS SimScale

  • Wind Turbine Simulation and Design
  • Kaplan Turbine: Working Principle, Design & Simulation
  • Low-Frequency Electromagnetics Simulation — Now in Your Browser
  • Employee Spotlight – Steven Lainé
  • SolidWorks Simulation: Seamless Proven Workflow with SimScale

RSS CG Channel

  • Autodesk adds MaterialX support to USD for 3ds Max 0.5
  • Rig and showcase 3D characters for free with AccuRig 1.3
  • Animate Anything uses AI to rig your 3D characters
  • See the new ZBrush features from ZBrush Summit 2023
  • Maxon announces ZBrush for iPad

RSS TechCrunch

  • Open Banking led to a FinTech boom — As Brite raises $60M, account-to-account payment grows
  • Indian fintech unicorn Slice secures rare approval to merge with bank
  • Krafton India launches gaming incubator to expand local ecosystem
  • Electric Hydrogen is the green hydrogen industry’s first unicorn
  • In latest Cruise incident, video shows pedestrian struck by human-driven car, then run over by robotaxi

RSS The Federalist

  • NFL Quarterbacks Must Choose Between Mega Contracts And Winning Rosters
  • Two Years Later, The Texas Heartbeat Act Has Saved Thousands Of Lives
  • This Activist Wife Schmoozes The Get-Trump White House While Her Prosecutor Husband Jails J6ers
  • Kevin McCarthy Loses Speakership Amid Gaetz-Led Charge
  • Haaland’s Activist Daughter Has Ties To Cuban Communist Solidarity Group

RSS Blender Nation

  • Pharmacy Or Drug Store 3D Assets [$]
  • Abstract Duality Typography in 3 minutes
  • "How I Animated this 3D Cinematic Scene in Blender"
  • Say goodbye to noise: Introducing Super Image Denoiser 4.0 with "SID-Temporal"
  • Interview with Dillon Goo

RSS Animation Guides

  • Sketch to Art: The AI Tool That’s Redefining Creativity
  • AI Video Generation: How to Produce Stunning Content in Minutes
  • Branding with Cartoons: Leveraging Cartoon Characters for Business Growth
  • Unlock the Secrets of Writing Great Prompts for Stable Diffusion AI Image Generation
  • Step-by-Step Guide to Installing and Using Stable Diffusion AI

Copyright © 2023 N23D Engineering Group.