Mathematics & Statistics

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class="nist-section-header__hero-img"> <div class="nist-block nist-block--no-margin"> <div class="entity-reference"> <img src="/web/20230212184619im_/https://www.nist.gov/sites/default/files/images/2022/04/13/Maths_1200x174.png" width="1200" height="174" alt="green peaks with some yellow and red near the top" loading="lazy" typeof="foaf:Image"/> </div> </div> </div> <div class="nist-section-header__main grid-container"> <div class="grid-row"> <div class="nist-section-header__title"> <h1 class="nist-page__title">Mathematics & Statistics</h1> </div> </div> </div> </div> </div> <div class="grid-container"> <div class="nist-page__region nist-page__region--topic-description padding-top-4 margin-top-1"> <div class="nist-region-heading"> <h2>Overview</h2> </div> <div class="grid-row"> <div class="tablet:grid-col-8 padding-right-5 margin-bottom-4"> <div class="text-with-summary"> <p>Using the latest mathematics approaches and computational methods, researchers at NIST provide state-of-the-art contributions that assist industry and academia in tackling some of the most difficult scientific, technical, and engineering problems and tasks.</p> <div class="nist-callout"> <h2>Happy 75th anniversary, math and stats at NIST!</h2> <p>To commemorate this anniversary, NIST has organized a three-day online symposium (June 28-30) featuring historical reflections, assessments of the impact of NIST work, presentations of current work, and examples of areas of future growth. <a data-entity-substitution="canonical" data-entity-type="node" data-entity-uuid="6e1229c9-588d-478d-8e53-5f5c1e3281e6" href="/web/20230212184619/https://www.nist.gov/news-events/events/2022/06/75th-anniversary-mathematics-and-statistics-nist" title="75th Anniversary of Mathematics and Statistics at NIST">Learn more and register to attend</a>.</p> </div> </div> </div> <div class="tablet:grid-col-4"> <div class="nist-block nist-block--no-margin"> <h2 class="nist-block__title">Featured Content</h2> <div class="nist-field nist-field--label-hidden nist-field--link-list link font-sans-sm"> <div class="nist-field__items"> <div class="nist-field__item"><a href="https://web.archive.org/web/20230212184619/https://dlmf.nist.gov/">Digital Library of Mathematical Functions</a></div> <div class="nist-field__item"><a href="https://web.archive.org/web/20230212184619/https://www.itl.nist.gov/div898/handbook/index.htm">NIST/SEMATECH Engineering Statistics Handbook</a></div> </div> </div> </div> </div> </div> </div> </div> <div class="bg-base-lightest padding-y-5 margin-y-4"> <div class="nist-page__region nist-page__region--topic-list grid-container"> <div class="views-element-container nist-block margin-bottom-0"> <div><div class="js-view-dom-id-c2ff4ecf0723d36ddd66d6b616e9a445a0ca0c0ca910ed06db07b4919821d124"> <div class="nist-block margin-bottom-0"> <div class="nist-region-heading"> <h2>Mathematics and statistics Topics</h2> </div> <ul class="add-list-reset link-list"> <div class="grid-row"> <div class="tablet:grid-col-6"> <li class="font-sans-md padding-bottom-205"><div class="views-field views-field-field-shared-section"><div class="field-content nist-icon nist-icon--before nist-icon--arrow-right2"><a href="/web/20230212184619/https://www.nist.gov/experiment-design" hreflang="en">Experiment design</a></div></div></li> </div> <div class="tablet:grid-col-6"> <li class="font-sans-md padding-bottom-205"><div class="views-field views-field-field-shared-section"><div class="field-content nist-icon nist-icon--before nist-icon--arrow-right2"><a href="/web/20230212184619/https://www.nist.gov/image-signal-processing" hreflang="en">Image & signal processing</a></div></div></li> </div> <div class="tablet:grid-col-6"> <li class="font-sans-md padding-bottom-205"><div class="views-field views-field-field-shared-section"><div class="field-content nist-icon nist-icon--before nist-icon--arrow-right2"><a href="/web/20230212184619/https://www.nist.gov/modeling-simulation-research" hreflang="en">Modeling & simulation research</a></div></div></li> </div> <div class="tablet:grid-col-6"> <li class="font-sans-md padding-bottom-205"><div class="views-field views-field-field-shared-section"><div class="field-content nist-icon nist-icon--before nist-icon--arrow-right2"><a href="/web/20230212184619/https://www.nist.gov/numerical-methods-software" hreflang="en">Numerical methods & software</a></div></div></li> </div> <div class="tablet:grid-col-6"> <li class="font-sans-md padding-bottom-205"><div class="views-field views-field-field-shared-section"><div class="field-content nist-icon nist-icon--before nist-icon--arrow-right2"><a href="/web/20230212184619/https://www.nist.gov/statistical-analysis" hreflang="en">Statistical analysis</a></div></div></li> </div> <div class="tablet:grid-col-6"> <li class="font-sans-md padding-bottom-205"><div class="views-field views-field-field-shared-section"><div class="field-content nist-icon nist-icon--before nist-icon--arrow-right2"><a href="/web/20230212184619/https://www.nist.gov/uncertainty-quantification" hreflang="en">Uncertainty quantification</a></div></div></li> </div> </div> </ul> </div> </div> </div> </div> </div> </div> <div class="nist-page__region nist-page__region--main"> <div class="nist-block"> <div class="grid-container margin-y-5"> <div class="paragraph paragraph--type--topic-research paragraph--view-mode--default"> <div class="nist-region-heading"> <h2>The Research</h2> </div> <div class="grid-row"> <div class="tablet:grid-col-8 padding-right-5 margin-y-2"> <h2 class="nist-block__title">Projects & Programs</h2> <article role="article" about="/programs-projects/nonlinear-optics-quantum-information-and-networking" class="nist-teaser"> <div class="nist-teaser__image"> <div class="entity-reference"> <a href="/web/20230212184619/https://www.nist.gov/programs-projects/nonlinear-optics-quantum-information-and-networking" hreflang="en"><img src="/web/20230212184619im_/https://www.nist.gov/sites/default/files/styles/thumbnail/public/images/2020/05/28/Kuo-Example_interconnects.jpg?itok=wtGOYpA5" width="100" height="76" alt="Image depiction of: To connect two nodes operating at different wavelengths, there are generally two strategies: (1) use quantum frequency conversion or quantum transduction to convert the wavelength of the photon emitted by one node to the wavelength of the second node, or (2) connect the two nodes using an entangled photon pair source whose two photons have wavelengths that match the two nodes. Both techniques involve nonlinear optics." loading="lazy" typeof="foaf:Image"/> </a> </div> </div> <div class="nist-teaser__content-wrapper"> <header> <h3 class="nist-teaser__title"><a href="/web/20230212184619/https://www.nist.gov/programs-projects/nonlinear-optics-quantum-information-and-networking"><span>Nonlinear Optics for Quantum Information and Networking</span> </a></h3> <div class="nist-teaser__type"> <div class="nist-badge display-inline-block margin-y-1 nist-badge--blue boolean">Ongoing</div> </div> </header> <div class="nist-teaser__content"> <div class="text-long"> Nonlinear optics offer ways to control and engineer the interconnects in a quantum network. In a hybrid quantum network where the quantum nodes operate at </div> </div> </div> </article> <article role="article" about="/programs-projects/high-performance-computing" class="nist-teaser"> <div class="nist-teaser__image"> <div class="entity-reference"> <a href="/web/20230212184619/https://www.nist.gov/programs-projects/high-performance-computing" hreflang="en"><img src="/web/20230212184619im_/https://www.nist.gov/sites/default/files/styles/thumbnail/public/images/2018/03/27/rheometer_20180322.png?itok=tSgJeA39" width="61" height="100" alt="A double-helix rheometer measuring the viscosity of mortar." loading="lazy" typeof="foaf:Image"/> </a> </div> </div> <div class="nist-teaser__content-wrapper"> <header> <h3 class="nist-teaser__title"><a href="/web/20230212184619/https://www.nist.gov/programs-projects/high-performance-computing"><span>High Performance Computing</span> </a></h3> <div class="nist-teaser__type"> <div class="nist-badge display-inline-block margin-y-1 nist-badge--blue boolean">Ongoing</div> </div> </header> <div class="nist-teaser__content"> <div class="text-long"> Our High Performance Computing (HPC) program enables work on challenging problems that are beyond the capacity and capability of desktop computing resources </div> </div> </div> </article> <article role="article" about="/programs-projects/special-functions" class="nist-teaser"> <div class="nist-teaser__image"> <div class="entity-reference"> <a href="/web/20230212184619/https://www.nist.gov/programs-projects/special-functions" hreflang="en"><img src="/web/20230212184619im_/https://www.nist.gov/sites/default/files/styles/thumbnail/public/images/itl/math/jacobianellipticfunctionsn_1.gif?itok=0gI4NwAI" width="100" height="69" loading="lazy" typeof="foaf:Image"/> </a> </div> </div> <div class="nist-teaser__content-wrapper"> <header> <h3 class="nist-teaser__title"><a href="/web/20230212184619/https://www.nist.gov/programs-projects/special-functions"><span>Special Functions</span> </a></h3> <div class="nist-teaser__type"> <div class="nist-badge display-inline-block margin-y-1 nist-badge--blue boolean">Ongoing</div> </div> </header> <div class="nist-teaser__content"> <div class="text-long"> This project will create a web-based portal enabling users to evaluate a large class of special functions to essentially arbitrary accuracy at user-defined </div> </div> </div> </article> <div class="link-list"><a href="/web/20230212184619/https://www.nist.gov/laboratories/projects-programs/topic/249011">View All Projects/Programs</a></div> </div> <div class="tablet:grid-col-4 margin-y-2"> <h2 class="nist-block__title">Additional Resources Links</h2> <div class="nist-field nist-field--label-hidden nist-field--link-list link nist-field--link-list font-sans-sm"> <div class="nist-field__items"> <div class="nist-field__item"><a href="/web/20230212184619/https://www.nist.gov/publications/search?k=&d%5Bmin%5D=&d%5Bmax%5D=&t=&a=&s=All&ta%5B0%5D=249011&ta%5B1%5D=249011&n=">Publications</a></div> </div> </div> </div> </div> </div> </div> <div class="paragraph paragraph--type--topic-featured paragraph--view-mode--default nist-content-row--width-full bg-base-lightest margin-y-5"> <div class="grid-container"> <div class="nist-card nist-card--horizontal nist-card--horizontal-full nist-card--base-lightest"> <div class="nist-card__inner"> <div class="nist-card__image"> <a href="/web/20230212184619/https://www.nist.gov/video/pioneering-life-ethel-marden"> <div class="entity-reference"> <figure class="nist-image"> <img src="/web/20230212184619im_/https://www.nist.gov/sites/default/files/styles/800w_x_400h/public/images/kaltura_import/2018/04/23/the_pioneering_life_of_ethel_marden_thumbnail.jpeg?itok=j86_X_jQ" width="800" height="400" alt="The Pioneering Life of Ethel Marden Thumbnail" title="The Pioneering Life of Ethel Marden Thumbnail" loading="lazy" typeof="foaf:Image"/> <figcaption class="nist-image__caption"> <div data-caption-editable="true" class="nist-image__caption-content"> </div> </figcaption> </figure> </div> </a> </div> <div class="nist-card__title"> <h3> The Pioneering Life of Ethel Marden </h3> </div> <div class="nist-card__content"> <div class="text-long"><p>Ethel Marden was a NIST mathematician who worked with SEAC, the nation's first computer with a memory, and lived a life that many would envy.</p></div> </div> <div class="nist-card__links"> <div class="nist-card__button"> <a href="/web/20230212184619/https://www.nist.gov/video/pioneering-life-ethel-marden" class="usa-button ">View video</a> </div> </div> </div> </div> </div> </div> <div class="grid-container margin-y-4"> <div class="nist-region-heading"> <h2>News</h2> </div> <div class="margin-bottom-5"> <div class="entity-reference"> <div class="nist-card nist-card--horizontal nist-card--horizontal-full"> <div class="nist-card__inner"> <div class="nist-card__image"> <a href="/web/20230212184619/https://www.nist.gov/blogs/taking-measure/future-now-spreading-word-about-post-quantum-cryptography"> <div class="entity-reference"> <img src="/web/20230212184619im_/https://www.nist.gov/sites/default/files/styles/600w_x_360h/public/images/2020/11/25/%C2%A9Yurchanka%20Siarhei_shutterstock_1210158169.jpg?itok=8bKB8G4G" width="600" height="360" alt="artist's concept of the inside of a quantum computer. A grid of blue computer chips with beams of light moving between them. " loading="lazy" typeof="foaf:Image"/> </div> </a> </div> <div class="nist-card__title"> <h3><span>The Future Is Now: Spreading the Word About Post-Quantum Cryptography</span> </h3> </div> <div class="nist-card__content"> <div class="text-with-summary">I consider myself a quiet guy — on a Friday night you can usually find me at home doing crossword puzzles. Public speaking doesn’t come naturally to me, and I’ve never really liked it. Like many people, I get really nervous. So, how did I find myself standing at a podium in front of hundreds of people in Fukuoka, Japan? I had never traveled that far away from home before. I was also pretty jet</div> </div> <div class="nist-card__links"> <div class="nist-card__button"> <a href="/web/20230212184619/https://www.nist.gov/blogs/taking-measure/future-now-spreading-word-about-post-quantum-cryptography" class="usa-button ">Read more</a> </div> </div> </div> </div> </div> </div> <div class="paragraph paragraph--type--dynamic-news-list-topic paragraph--view-mode--default"> <div class="views-element-container"><div class="js-view-dom-id-0e5d255c63407c997d8dd376265a96aea4d499e9e6c796c714f1bfe785538427"> <div class="grid-row grid-gap-2"> <div class="nist-card tablet:grid-col-4 nist-card--topic "> <div class="nist-card__inner"> <div class="nist-card__image"> <a href="/web/20230212184619/https://www.nist.gov/news-events/news/2023/01/spotlight-meet-mentor-summer-undergraduates-nist-quantum-physicist-krister"> <div class="entity-reference"> <img src="/web/20230212184619im_/https://www.nist.gov/sites/default/files/styles/800w_x_400h/public/images/2023/01/23/DSC_1600.jpg?itok=pvvHrv22" width="800" height="400" alt="Man wearing safety glasses leans toward a tabletop optical laser setup." loading="lazy" typeof="foaf:Image"/> </div> </a> </div> <div class="nist-card__title padding-y-5"> <h3><span property="schema:name">Spotlight: Meet a Mentor for Summer Undergraduates: NIST Quantum Physicist Krister Shalm</span> </h3> </div> <div class="nist-card__links"> <div class="nist-card__button"> <a href="/web/20230212184619/https://www.nist.gov/news-events/news/2023/01/spotlight-meet-mentor-summer-undergraduates-nist-quantum-physicist-krister" class="usa-button ">Read more</a> </div> </div> </div> </div> <div class="nist-card tablet:grid-col-4 nist-card--topic "> <div class="nist-card__inner"> <div class="nist-card__image"> <a href="/web/20230212184619/https://www.nist.gov/news-events/news/2022/09/hooked-photonics-math-rescue"> <div class="entity-reference"> <img src="/web/20230212184619im_/https://www.nist.gov/sites/default/files/images/2022/09/28/Bragg_FINAL.gif" width="2958" height="1590" alt="bragg grating" loading="lazy" typeof="foaf:Image"/> </div> </a> </div> <div class="nist-card__title padding-y-5"> <h3><span property="schema:name">Hooked on Photonics? 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