Juliais ahigh-level,general-purpose[17]dynamicprogramming language,still designed to be fast and productive,[18]for e.g. data science, artificial intelligence, machine learning, modeling and simulation, most commonly used fornumerical analysisandcomputational science.[19][20][21]
Paradigm | Multi-paradigm:multiple dispatch(primary paradigm),functional,array,procedural(imperative),structured,reflective,meta,multistaged[1] |
---|---|
Designed by | Jeff Bezanson,Alan Edelman,Stefan Karpinski,Viral B. Shah |
Developer | Jeff Bezanson,Stefan Karpinski,Viral B. Shah,and other contributors[2][3] |
First appeared | 2012[4] |
Stable release | |
Preview release | |
Typing discipline | Dynamic,[9]inferred,optional,nominative,parametric,strong[9] |
Implementation language | Julia,C,C++,LLVM,[10]Scheme(was used the parser; almost exclusively) |
Platform | Tier 1:x86-64,IA-32,Apple silicon(ARM64)Macs; Nvidia GPUs/CUDA(on Linux)[11] Tier 2:FreeBSD,64-bit Armon Linux, Apple GPUs; Intel GPUs/OneAPI6.2+ and Nvidia GPUs (on Windows) Tier 3: 32-bitArm;64-bitRISC-VandPowerPC;and AMD GPUs/ROCm5.3+. |
OS | Linux,macOS,WindowsandFreeBSD |
License | MIT |
Filename extensions | .jl |
Website | JuliaLang.org |
Influenced by | |
Distinctive aspects of Julia's design include a type system withparametric polymorphismand the use ofmultiple dispatchas a coreprogramming paradigm,a defaultjust-in-time(JIT) compiler[17][22](with support forahead-of-time compilation[23][24][25]) and anefficient garbage collection.[26]Notably Julia does not support classes with encapsulated methods and instead it relies on structs with generic methods/functions not tied to them.
By default, Julia is run similarly to scripting languages, using its runtime, and allows forinteractions,[23]but Julia programs/source codecan also optionally be sent to users in one ready-to-install/run file, which can be made quickly, not needing anything preinstalled.[27]Julia programs can also be (separately) compiled tobinary executables,even allowing no-source-code distribution, and the executables can get much smaller with Julia 1.12. Such compilation is not needed for speed, though it can decrease constant-factor startup cost, since Julia is also compiled when running interactively, but it can help with hiding source code. Features of the language can be separately compiled, so Julia can be used, for example, with its runtime or without it (which allows for smaller executables and libraries but is limited in capabilities).
Julia programs can reuse libraries from other languages by calling them, e.g. callingCorRustlibraries, and Julia (libraries) can also be called from other languages, e.g.PythonandR,and several Julia packages have been made easily available from those languages, in the form of Python and Rlibrariesfor corresponding Julia packages. Calling in either direction has been implemented for many languages, not just those.
Julia'sVisual Studio Codeextension provides a fully-featuredintegrated development environmentwith "built-in dynamic autocompletion, inline results, plot pane, integrated REPL, variable view, code navigation, and many other advanced language features"[28]e.g. debugging is possible,linting,andprofiling.[29][30][31][32]
History
editWork on Julia began in 2009, whenJeff Bezanson,Stefan Karpinski,Viral B. Shah,andAlan Edelmanset out to create a free language that was both high-level and fast. On 14 February 2012, the team launched a website with a blog post explaining the language's mission.[4]In an interview withInfoWorldin April 2012, Karpinski said of the name "Julia": "There's no good reason, really. It just seemed like a pretty name."[20]Bezanson said he chose the name on the recommendation of a friend,[33]then years later wrote:
Maybe julia stands for "Jeff'suncommon lispis automated "?[34]
Julia'ssyntaxis now considered stable, since version 1.0 in 2018, and Julia has abackward compatibilityguarantee for 1.x and also a stability promise for the documented (stable)API,while in the years before in the early development prior to 0.7 the syntax (and semantics) was changed in new versions. All of the (registered package)ecosystemuses the new and improved syntax, and in most cases relies on new APIs that have been added regularly, and in some cases minor additional syntax added in a forward compatible way e.g. in Julia 1.7.
In the 10 years since the 2012 launch of pre-1.0 Julia, the community has grown. The Julia package ecosystem has over 11.8 million lines of code (including docs and tests).[35]The JuliaConacademic conferencefor Julia users and developers has been held annually since 2014 with JuliaCon2020[36]welcoming over 28,900 unique viewers,[37]and then JuliaCon2021 breaking all previous records (with more than 300 JuliaCon2021 presentations available for free on YouTube, up from 162 the year before), and 43,000 unique viewers during the conference.[38]
Three of the Julia co-creators are the recipients of the 2019James H. Wilkinson Prize for Numerical Software(awarded every four years) "for the creation of Julia, an innovative environment for the creation of high-performance tools that enable the analysis and solution of computational science problems."[39]Also, Alan Edelman, professor ofapplied mathematicsatMIT,has been selected to receive the 2019IEEE Computer SocietySidney Fernbach Award"for outstanding breakthroughs in high-performance computing, linear algebra, and computational science and for contributions to the Julia programming language."[40]
Both Julia 0.7[41]and version 1.0 were released on 8 August 2018. Work on Julia 0.7 was a "huge undertaking" (e.g., because of an "entirely new optimizer" ), and some changes were made to semantics, e.g. theiterationinterface was simplified.[42]
Julia 1.6 was the largest release since 1.0, and it was thelong-term support(LTS) version for the longest time, faster on many fronts, e.g. introduced parallel precompilation and faster loading of packages, in some cases "50x speedup in load times for large trees of binary artifacts".[43]As of version 1.7 Julia development is back totime-based releases.[44]Julia 1.7.0 was released in November 2021 with many changes, e.g. a new fasterrandom-number generator.Julia 1.7.3 was released on 25 May 2022, fixing some issues, including at least one security update,[45]and 1.7.x is no longer supported. Julia 1.8 was released in 2022 (and versions up to 1.8.5 as a followup in January 2023,[46]both fixing bugs (backporting) and "invalidations", thus compiling faster), with improvements for distributing Julia programs without source code, and compiler speedup, in some cases by 25%,[47]and more controllableinlining(i.e. now also allowing applying@inline
at the call site, not just on the function itself). Julia 1.9.0 was released on 7 May 2023. It has many improvements, such as the ability to precompile packages to native machine code (older Julia versions also have precompilation for packages, but only partial, never fully to native code, so those earlier versions had a "first use" penalty, slowing down while waiting to fully compile). Precompiled packages, since version 1.9, can be up to hundreds of times faster on first use (e.g. for CSV.jl and DataFrames.jl), and to improve precompilation of packages a new package PrecompileTools.jl has been introduced. Julia 1.10.0 was released on 25 December 2023 (and Julia 1.10.5 update on 27 August 2024) with many new features, e.g. parallel garbage collection, and improved package load times and a new parser with better error messages and improved stacktrace rendering.[48]
Julia 1.11.0 was released on 7 October 2024 (and 1.11.1 on 16 October), and with it 1.10.5 became the nextlong-term support(LTS) version (i.e. those are the only two supported versions), since replaced by 1.10.6 released on 28 October, and 1.6 is no longer an LTS version. Julia 1.11 adds e.g. a newpublic
keyword to signal safe public API (Julia users are advised to use such API, not internals, of Julia or packages, and package authors advised to use the keyword, generally indirectly, e.g. prefixed with the@compat
macro, fromCompat.jl,to also support older Julia versions, at least the LTS version). Julia 1.11.1 has much improved startup (over 1.11.0 that had a regression), and over 1.10, and this can be important for some benchmarks.
Some users may want to postopone upgrading to 1.11 (e.g. those calling Julia from R), because of known temporary package incompatibility.
Much smaller binary executables are possible withjuliac
which is only available in the upcoming Julia 1.12 (the current "nightly" version).
JuliaCon
editSince 2014,[49]the Julia Community has hosted an annual Julia Conference focused on developers and users. The first JuliaCon took place in Chicago and kickstarted the annual occurrence of the conference. Since 2014, the conference has taken place across a number of locations including MIT[50]and the University of Maryland, Baltimore.[51]The event audience has grown from a few dozen people to over 28,900 unique attendees[52]during JuliaCon 2020, which took place virtually. JuliaCon 2021 also took place virtually[53]with keynote addresses from professorsWilliam Kahan,the primary architect of theIEEE 754floating-point standard (which virtually all CPUs and languages, including Julia, use),[54]Jan Vitek,[55]XiaoyeSherry Li,and Soumith Chintala, a co-creator ofPyTorch.[56]JuliaCon grew to 43,000 unique attendees and more than 300 presentations (still freely accessible, plus for older years). JuliaCon 2022 will also be virtual held between July 27 and July 29, 2022, for the first time in several languages, not just in English.
Sponsors
editThe Julia language became a NumFOCUS fiscally sponsored project in 2014 in an effort to ensure the project's long-term sustainability.[57]Jeremy Kepner atMIT Lincoln Laboratorywas the founding sponsor of the Julia project in its early days. In addition, funds from theGordon and Betty Moore Foundation,theAlfred P. Sloan Foundation,Intel,and agencies such asNSF,DARPA,NIH,NASA,andFAAhave been essential to the development of Julia.[58]Mozilla,the maker of Firefox web browser, with its research grants for H1 2019, sponsored "a member of the official Julia team" for the project "Bringing Julia to the Browser",[59]meaning to Firefox and other web browsers.[60][61][62][63]The Julia language is also supported by individual donors on GitHub.[64]
The Julia company
editJuliaHub, Inc. was founded in 2015 as Julia Computing, Inc. byViral B. Shah,Deepak Vinchhi,Alan Edelman,Jeff Bezanson,Stefan KarpinskiandKeno Fischer.[65][66]
In June 2017, Julia Computing raised US$4.6million in seed funding fromGeneral Catalystand Founder Collective,[67]the same month was "granted $910,000 by theAlfred P. Sloan Foundationto supportopen-sourceJulia development, including $160,000 to promote diversity in the Julia community ",[68]and in December 2019 the company got $1.1million funding from the US government to "develop a neural componentmachine learningtool to reduce the total energy consumption of heating, ventilation, and air conditioning (HVAC) systems in buildings ".[69]In July 2021, Julia Computing announced they raised a $24 millionSeries A roundled by Dorilton Ventures,[70]which also ownsFormula 1teamWilliams Racing,that partnered with Julia Computing. Williams' Commercial Director said: "Investing in companies building best-in-class cloud technology is a strategic focus for Dorilton and Julia's versatile platform, with revolutionary capabilities in simulation and modelling, is hugely relevant to our business. We look forward to embedding Julia Computing in the world's most technologically advanced sport".[71]In June 2023, JuliaHub received (again, now under its new name) a $13 million strategic new investment led by AE Industrial Partners HorizonX ( "AEI HorizonX" ). AEI HorizonX is a venture capital investment platform formed in partnership withThe Boeing Company,which uses Julia.[72]Tim Holy's work (atWashington University in St. Louis's Holy Lab) on Julia 1.9 (improving responsiveness) was funded by theChan Zuckerberg Initiative.
Language features
editJulia is ageneral-purpose programming language,[73]while also originally designed for numerical/technical computing. It is also useful for low-levelsystems programming,[74]as aspecification language,[75]high-level synthesis (HLS) tool (for hardware, e.g.FPGAs),[76]and for web programming[77]at both server[78][79]and client[80][81]side.
The main features of the language are:
- Multiple dispatch: providing ability to define function behavior across combinations of argument types
- Dynamic typesystem: types for documentation, optimization, and dispatch
- Performance approaching that ofstatically-typedlanguages like C
- A built-inpackage manager
- Lisp-like macros and othermetaprogrammingfacilities
- Designed forparallelanddistributed computing
- Coroutines:lightweightgreenthreading
- Automatic generation of code for different argument types
- Extensible conversions and promotions for numeric and other types
Multiple dispatch (also termedmultimethodsin Lisp) is ageneralizationofsingle dispatch– thepolymorphic mechanismused in commonobject-oriented programming(OOP) languages, such asPython,C++,Java,JavaScript,andSmalltalk– that usesinheritance.In Julia, all concrete types aresubtypesof abstract types, directly or indirectly subtypes of theAny
type, which is the top of the type hierarchy. Concrete types can not themselves be subtyped the way they can in other languages; composition is used instead (see alsoinheritance vs subtyping).
By default, the Julia runtime must be pre-installed as user-provided source code is run. Alternatively, Julia (GUI) apps can be quickly bundled up into a single file with AppBundler.jl[27]for "building Julia GUI applications in modern desktop application installer formats. It uses Snap for Linux,MSIXfor Windows, and DMG for MacOS as targets. It bundles full Julia within the app ".[82]PackageCompiler.jl can build standaloneexecutablesthat need no Julia source code to run.[23]
In Julia, everything is an object, much like object-oriented languages; however, unlike most object-oriented languages, all functions usemultiple dispatchto select methods, rather than single dispatch.
Most programming paradigms can be implemented using Julia'shomoiconicmacros and packages. Julia'ssyntactic macros(used formetaprogramming), like Lisp macros, are more powerful thantext-substitution macrosused in thepreprocessorof some other languages such as C, because they work at the level ofabstract syntax trees(ASTs). Julia's macro system ishygienic,but also supports deliberate capture when desired (like foranaphoric macros) using theesc
construct.
Julia draws inspiration from various dialects of Lisp, includingSchemeandCommon Lisp,and it shares many features withDylan,also a multiple-dispatch-oriented dynamic language (which features aninfixsyntax rather than a Lisp-like prefix syntax, while in Julia "everything"[83]is anexpression), and withFortress,another numerical programming language (which features multiple dispatch and a sophisticated parametric type system). WhileCommon Lisp Object System(CLOS) adds multiple dispatch to Common Lisp, not all functions are generic functions.
In Julia, Dylan, and Fortress, extensibility is the default, and the system's built-in functions are all generic and extensible. In Dylan, multiple dispatch is as fundamental as it is in Julia: all user-defined functions and even basic built-in operations like+
are generic. Dylan's type system, however, does not fully support parametric types, which are more typical of theML lineage of languages.By default, CLOS does not allow for dispatch on Common Lisp's parametric types; such extended dispatch semantics can only be added as an extension through theCLOS Metaobject Protocol.By convergent design, Fortress also features multiple dispatch on parametric types; unlike Julia, however, Fortress is statically rather than dynamically typed, with separate compiling and executing phases. The language features are summarized in the following table:
Language | Type system | Generic functions | Parametric types |
---|---|---|---|
Julia | Dynamic | Default | Yes |
Common Lisp | Dynamic | Opt-in | Yes (but no dispatch) |
Dylan | Dynamic | Default | Partial (no dispatch) |
Fortress | Static | Default | Yes |
An example of the extensibility of Julia, the Unitful.jl package adds support for physicalunits of measurementto the language.
Interoperability
editJulia has built-in support for callingCorFortranlanguage libraries using the@ccall
macro. Additional libraries allow users to work withPython,[84]R,[85]C++,[86]Java,[87]andSQL.[88][89][90][91]
Separately-compiled executables option
editJulia can be compiled to binaryexecutableswith PackageCompiler.jl.[23]Smaller executables can also be written using a static subset of the language provided by StaticCompiler.jl that does not supportruntime dispatch(nor garbage collection, since excludes the runtime that provides it).[92]
Interaction
editThe Julia official distribution includes an interactive command-lineread–eval–print loop(REPL),[93]with a searchable history,tab completion,and dedicated help andshellmodes,[94]which can be used to experiment and test code quickly.[95]The following fragment represents a sample session example where strings are concatenated automatically by println:[96]
julia>p(x)=2x^2+1;f(x,y)=1+2p(x)y
julia>println("Hello world!","I'm on cloud",f(0,4),"as Julia supports recognizable syntax!")
Hello world! I'm on cloud 9 as Julia supports recognizable syntax!
The REPL gives user access to the system shell and to help mode, by pressing;
or?
after the prompt (preceding each command), respectively. It also keeps the history of commands, including between sessions.[97]Code can be tested inside Julia's interactive session or saved into a file with a.jl
extension and run from the command line by typing:[83]
$julia<filename>
Julia usesUTF-8andLaTeXcodes, allowing it to support common math symbols for many operators, such as ∈ for thein
operator, typable with\in
then pressingTab ↹(i.e. usesLaTeXcodes, or also possible by simply copy-pasting, e.g. √ and ∛ possible forsqrtandcbrtfunctions). Julia has support for the latest major release Unicode 15.0 (Julia 1.11-DEV supports latest 15.1 point release[98])[99]for the languages of the world, even for source code, e.g. variable names (while it's recommended to use English for public code, and e.g. package names).
Julia is supported byJupyter,an online interactive "notebooks" environment,[100]andPluto.jl,a "reactive notebook" (where notebooks are saved as pure Julia files), a possible replacement for the former kind.[101]In addition Posit's (formerlyRStudioInc's) Quarto publishing system supports Julia, Python, R and ObservableJavaScript(those languages have official support by the company, and can even be weaved together in the same notebook document, more languages are unofficially supported).[102][103]
The REPL can be extended with additional modes, and has been with packages, e.g. with anSQLmode,[104]for database access, and RCall.jl adds anR mode,to work with theR language.[105]
Use with other languages
editJulia is in practiceinteroperablewith other languages, in fact the majority of the top 20 languages in popular use. Julia can be used to call shared library functions individually, such as those written in C or Fortran, and packages are available to allow calling other languages (which do not provide C-exported functions directly) e.g. Python (with PythonCall.jl), R,[106]MATLAB, C# (and other.NET languages with DotNET.jl, from them with JdotNET), JavaScript, Java (and other JVM languages, such asScalawith JavaCall.jl). And packages for other languages allow to call to Julia, e.g. from Python, R (to Julia 1.10.x currently possible[107]),Rust,Ruby, or C#. Such as with juliacall (part of PythonCall.jl) to call from Python and a different JuliaCall package for calling, Julia up to 1.10.x, from R. Julia has also been used for hardware, i.e. to compile toVHDL,as ahigh-level synthesistool, for exampleFPGAs.[76]
Julia has packages supporting markup languages such asHTML(and also forHTTP),XML,JSONandBSON,and fordatabases(such as PostgreSQL,[108]Mongo,[109]Oracle, including forTimesTen,[110]MySQL, SQLite, Microsoft SQL Server,[109]Amazon Redshift, Vertica, ODBC) and web use in general.[111][112]
Package system
editJulia has a built-inpackage managerand includes a default registry system.[113]Packages are most often distributed as source code hosted onGitHub,though alternatives can also be used just as well. Packages can also be installed as binaries, using artifacts.[114]Julia's package manager is used to query and compile packages, as well as managing environments. Federated package registries are supported, allowing registries other than the official to be added locally.[115]
Implementation
editJulia's core is implemented in Julia andC,together withC++for theLLVMdependency. The code parsing, code-lowering, and bootstrapping were implemented in FemtoLisp, aSchemedialect, up to version 1.10.[116]Since that version the new pure-Julia packageJuliaSyntax.jl,is used for the parsing (while the old one can still be chosen)[117]which improves speed and "greatly improves parser error messages in various cases".[118]The LLVM compiler infrastructure project is used as theback endfor generating optimizedmachine codefor all commonly-used platforms. With some exceptions, thestandard libraryis implemented in Julia.
Current and future platforms
editJulia has tier 1macOSsupport, for 64-bitApple SiliconMacs, natively (previously suchApple M1-based Macs were only supported byrunning inRosetta 2emulation[119][120]), and also fully supports Intel-based Macs.Windows on ARMhas no official support yet. Julia has "initial support of OpenBSD in julia." but more is coming to make it actually work:https://github.com/JuliaLang/julia/issues/53632-->
Julia has four support tiers.[121]AllIA-32processors completely implementing thei686subarchitecture are supported and all 64-bitx86-64(akaamd64), i.e. all less than about a decade old are supported.Armv8(AArch64) processors are supported on first tier (for macOS); otherwise second tier on Linux, and ARMv7 (AArch32) on third tier.[122]Hundreds of packages areGPU-accelerated:[123]Nvidia GPUs have support withCUDA.jl(tier 1 on 64-bit Linux and tier 2 on 64-bit Windows, the package implementingPTX,for compute capability 3.5 (Kepler) or higher; both require CUDA 11+, older package versions work down to CUDA 9). There are also additionally packages supporting other accelerators, such as Google'sTPUs,[124]and some Intel (integrated) GPUs, throughoneAPI.jl,[125]and AMD's GPUs have support with e.g.OpenCL;and experimental support for the AMDROCmstack.[126]
On some platforms, Julia may need to be compiled from source code (e.g., the originalRaspberry Pi), with specific build options, which has been done and unofficial pre-built binaries (and build instructions) are available.[127][128]Julia has been built for several ARM platforms, from small Raspberry Pis to the world's fastest (at one point, until recently) supercomputerFugaku's ARM-basedA64FX.[129]PowerPC (64-bit) has tier 3 support, meaning it "may or may not build". Julia is now supported inRaspbian[130]while support is better for newer Pis, e.g., those with Armv7 or newer; the Julia support is promoted by theRaspberry Pi Foundation.[131]Julia has also been built for 64-bitRISC-V,[132][133]that has some supporting code in core Julia.
While Julia requires anoperating systemby default, and has no official support to run without or onembedded systemplatforms such asArduino,Julia code has still been run on it, with some limitations, i.e. on a baremetal 16MHz8-bit(ATmega328P)AVR-microcontrollerArduino with 2 KB RAM (plus 32 KB of flash memory).[134][135]
Adoption
editJulia has been adopted at many universities includingMIT,Stanford,UC Berkeley,Ferdowsi University of Mashhadand theUniversity of Cape Town.Large private firms across many sectors have adopted the language includingAmazon,IBM,JP MorganAI Research,[136]andASML.Julia has also been used by government agencies includingNASAand theFAA,as well as every US national energy laboratory.[18][137]
Scientific computing and engineering
edit- Amazon,forquantum computing[138]andmachine learningthroughAmazon SageMaker[139]
- ASML,forhard real-timeprogramming with their machines[140]
- The Climate Modeling Alliance[141]for climate change modeling[142]
- CERN,to analyze data from theLarge Hadron Collider(LHCb experiment)[143][144][145][146][147][148]
- NASA and theJet Propulsion Laboratoryuse Julia to model spacecraft separation dynamics,[149][150][151]analyzeTRAPPISTexoplanetdatasets,[152][153]and analyzecosmic microwave backgrounddata from theBig Bang[154]
- The BrazilianINPE,for space missions andsatellitesimulations[155]
- Embeddedhardware to plan and execute flight of autonomous U.S.Air Force Research LaboratoryVTOLdrones[156]
Pharmaceuticals and drug development
editJulia is widely used for drug development in the pharmaceutical industry, having been adopted byModerna,Pfizer,AstraZeneca,Procter & Gamble,andUnited Therapeutics.[157][158]
Economics, finance, and political science
edit- TheFederal Reserve Bank of New York,for macroeconomic modeling in Julia since 2015, including estimates ofCOVID-19shocks in 2021[159]
- Also theBank of Canada,central bank,for macroeconomic modeling[160]
- BlackRock,the world's largest asset manager, forfinancial time-series analysis[161]
- Aviva,theUK's largest general insurer, for actuarial calculations[161]
- Mitre Corporation,for verification of published election results[162]
- Nobel laureateThomas J. Sargent,formacroeconometric modeling[163]
See also
edit- Comparison of numerical-analysis software
- Comparison of statistical packages
- Differentiable programming
- JuMP– an algebraic modeling language for mathematical optimization embedded in Julia
- Python
- Nim
- Ring
- Mojo
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running language interpreters in WebAssembly. To further increase access to leading data science tools, we're looking for someone to port R or Julia to WebAssembly and to attempt to provide a level 3 language plugin for Iodide: automatic conversion of data basic types between R/Julia and Javascript, and the ability to share class instances between R/Julia and Javascript.
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The flight test team was able to demonstrate… a vertical takeoff and landing vehicle with both electric and conventional fuel propulsion systems onboard. The[uncrewed aerial system]was able to plan and execute these missions autonomously using onboard hardware. It was the first time the Julia programming language was flown on the embedded hardware - algorithms were precompiled ahead of time.
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Further reading
edit- Nagar, Sandeep (2017).Beginning Julia Programming: For Engineers and Scientists.Springer.ISBN978-1-4842-3171-5.
- Bezanson, J; Edelman, A; Karpinski, S; Shah, V. B (2017). "Julia: A fresh approach to numerical computing".SIAM Review.59(1): 65–98.arXiv:1411.1607.CiteSeerX10.1.1.760.8894.doi:10.1137/141000671.S2CID13026838.
- Joshi, Anshul (2016).Julia for Data Science - Explore the world of data science from scratch with Julia by your side.Packt.ISBN978-1-78355-386-0.
- Tobin A Driscoll and Richard J. Braun (Aug. 2022). "Fundamentals of Numerical Computation: Julia Edition". SIAM.ISBN978-1-611977-00-4.
- C. T. Kelley (2022). "Solving Nonlinear Equations with Iterative Methods: Solvers and Examples in Julia", SIAM.ISBN978-1-611977-26-4.
- Kalicharan, Noel (2021).Julia - Bit by Bit.Undergraduate Topics in Computer Science. Springer.doi:10.1007/978-3-030-73936-2.ISBN978-3-030-73936-2.S2CID235917112.
- Clemens Heitzinger (2022): "Algorithms with Julia", Springer, ISBN 978-3-031-16559-7.