PageSourceSearch

http://www.kevinhouston.net/blog/

html kevinhouston.net collected 2026-10-02 14:46:57 UTC 60,655 bytes, 592 lines download raw bytes

1<!DOCTYPE html>
2<html lang="en-US">
3<head>
4    <meta charset="UTF-8">
5    <meta name="viewport" content="width=device-width, initial-scale=1">
6    <link rel="profile" href="http://gmpg.org/xfn/11">
7    <title>Kevin Houston &#8211; Thinking mathematically&#8230;</title>
8<meta name='robots' content='max-image-preview:large' />
9<link rel="alternate" type="application/rss+xml" title="Kevin Houston &raquo; Feed" href="https://www.kevinhouston.net/blog/feed/" />
10<link rel="alternate" type="application/rss+xml" title="Kevin Houston &raquo; Comments Feed" href="https://www.kevinhouston.net/blog/comments/feed/" />
11<script type="text/javascript">
12/* <![CDATA[ */
13window._wpemojiSettings = {"baseUrl":"https:\/\/s.w.org\/images\/core\/emoji\/15.0.3\/72x72\/","ext":".png","svgUrl":"https:\/\/s.w.org\/images\/core\/emoji\/15.0.3\/svg\/","svgExt":".svg","source":{"concatemoji":"http:\/\/www.kevinhouston.net\/blog\/wp-includes\/js\/wp-emoji-release.min.js?ver=6.6.9"}};
14/*! This file is auto-generated */
15!function(i,n){var o,s,e;function c(e){try{var t={supportTests:e,timestamp:(new Date).valueOf()};sessionStorage.setItem(o,JSON.stringify(t))}catch(e){}}function p(e,t,n){e.clearRect(0,0,e.canvas.width,e.canvas.height),e.fillText(t,0,0);var t=new Uint32Array(e.getImageData(0,0,e.canvas.width,e.canvas.height).data),r=(e.clearRect(0,0,e.canvas.width,e.canvas.height),e.fillText(n,0,0),new Uint32Array(e.getImageData(0,0,e.canvas.width,e.canvas.height).data));return t.every(function(e,t){return e===r[t]})}function u(e,t,n){switch(t){case"flag":return n(e,"\ud83c\udff3\ufe0f\u200d\u26a7\ufe0f","\ud83c\udff3\ufe0f\u200b\u26a7\ufe0f")?!1:!n(e,"\ud83c\uddfa\ud83c\uddf3","\ud83c\uddfa\u200b\ud83c\uddf3")&&!n(e,"\ud83c\udff4\udb40\udc67\udb40\udc62\udb40\udc65\udb40\udc6e\udb40\udc67\udb40\udc7f","\ud83c\udff4\u200b\udb40\udc67\u200b\udb40\udc62\u200b\udb40\udc65\u200b\udb40\udc6e\u200b\udb40\udc67\u200b\udb40\udc7f");case"emoji":return!n(e,"\ud83d\udc26\u200d\u2b1b","\ud83d\udc26\u200b\u2b1b")}return!1}function f(e,t,n){var r="undefined"!=typeof WorkerGlobalScope&&self instanceof WorkerGlobalScope?new OffscreenCanvas(300,150):i.createElement("canvas"),a=r.getContext("2d",{willReadFrequently:!0}),o=(a.textBaseline="top",a.font="600 32px Arial",{});return e.forEach(function(e){o[e]=t(a,e,n)}),o}function t(e){var t=i.createElement("script");t.src=e,t.defer=!0,i.head.appendChild(t)}"undefined"!=typeof Promise&&(o="wpEmojiSettingsSupports",s=["flag","emoji"],n.supports={everything:!0,everythingExceptFlag:!0},e=new Promise(function(e){i.addEventListener("DOMContentLoaded",e,{once:!0})}),new Promise(function(t){var n=function(){try{var e=JSON.parse(sessionStorage.getItem(o));if("object"==typeof e&&"number"==typeof e.timestamp&&(new Date).valueOf()<e.timestamp+604800&&"object"==typeof e.supportTests)return e.supportTests}catch(e){}return null}();if(!n){if("undefined"!=typeof Worker&&"undefined"!=typeof OffscreenCanvas&&"undefined"!=typeof URL&&URL.createObjectURL&&"undefined"!=typeof Blob)try{var e="postMessage("+f.toString()+"("+[JSON.stringify(s),u.toString(),p.toString()].join(",")+"));",r=new Blob([e],{type:"text/javascript"}),a=new Worker(URL.createObjectURL(r),{name:"wpTestEmojiSupports"});return void(a.onmessage=function(e){c(n=e.data),a.terminate(),t(n)})}catch(e){}c(n=f(s,u,p))}t(n)}).then(function(e){for(var t in e)n.supports[t]=e[t],n.supports.everything=n.supports.everything&&n.supports[t],"flag"!==t&&(n.supports.everythingExceptFlag=n.supports.everythingExceptFlag&&n.supports[t]);n.supports.everythingExceptFlag=n.supports.everythingExceptFlag&&!n.supports.flag,n.DOMReady=!1,n.readyCallback=function(){n.DOMReady=!0}}).then(function(){return e}).then(function(){var e;n.supports.everything||(n.readyCallback(),(e=n.source||{}).concatemoji?t(e.concatemoji):e.wpemoji&&e.twemoji&&(t(e.twemoji),t(e.wpemoji)))}))}((window,document),window._wpemojiSettings);
16/* ]]> */
17</script>
17
18<style id='wp-emoji-styles-inline-css' type='text/css'>
19
20	img.wp-smiley, img.emoji {
21		display: inline !important;
22		border: none !important;
23		box-shadow: none !important;
24		height: 1em !important;
25		width: 1em !important;
26		margin: 0 0.07em !important;
27		vertical-align: -0.1em !important;
28		background: none !important;
29		padding: 0 !important;
30	}
31</style>
32<link rel='stylesheet' id='wp-block-library-css' href='http://www.kevinhouston.net/blog/wp-includes/css/dist/block-library/style.min.css?ver=6.6.9' type='text/css' media='all' />
33<style id='wp-block-library-theme-inline-css' type='text/css'>
34.wp-block-audio :where(figcaption){color:#555;font-size:13px;text-align:center}.is-dark-theme .wp-block-audio :where(figcaption){color:#ffffffa6}.wp-block-audio{margin:0 0 1em}.wp-block-code{border:1px solid #ccc;border-radius:4px;font-family:Menlo,Consolas,monaco,monospace;padding:.8em 1em}.wp-block-embed :where(figcaption){color:#555;font-size:13px;text-align:center}.is-dark-theme .wp-block-embed :where(figcaption){color:#ffffffa6}.wp-block-embed{margin:0 0 1em}.blocks-gallery-caption{color:#555;font-size:13px;text-align:center}.is-dark-theme .blocks-gallery-caption{color:#ffffffa6}:root :where(.wp-block-image figcaption){color:#555;font-size:13px;text-align:center}.is-dark-theme :root :where(.wp-block-image figcaption){color:#ffffffa6}.wp-block-image{margin:0 0 1em}.wp-block-pullquote{border-bottom:4px solid;border-top:4px solid;color:currentColor;margin-bottom:1.75em}.wp-block-pullquote cite,.wp-block-pullquote footer,.wp-block-pullquote__citation{color:currentColor;font-size:.8125em;font-style:normal;text-transform:uppercase}.wp-block-quote{border-left:.25em solid;margin:0 0 1.75em;padding-left:1em}.wp-block-quote cite,.wp-block-quote footer{color:currentColor;font-size:.8125em;font-style:normal;position:relative}.wp-block-quote.has-text-align-right{border-left:none;border-right:.25em solid;padding-left:0;padding-right:1em}.wp-block-quote.has-text-align-center{border:none;padding-left:0}.wp-block-quote.is-large,.wp-block-quote.is-style-large,.wp-block-quote.is-style-plain{border:none}.wp-block-search .wp-block-search__label{font-weight:700}.wp-block-search__button{border:1px solid #ccc;padding:.375em .625em}:where(.wp-block-group.has-background){padding:1.25em 2.375em}.wp-block-separator.has-css-opacity{opacity:.4}.wp-block-separator{border:none;border-bottom:2px solid;margin-left:auto;margin-right:auto}.wp-block-separator.has-alpha-channel-opacity{opacity:1}.wp-block-separator:not(.is-style-wide):not(.is-style-dots){width:100px}.wp-block-separator.has-background:not(.is-style-dots){border-bottom:none;height:1px}.wp-block-separator.has-background:not(.is-style-wide):not(.is-style-dots){height:2px}.wp-block-table{margin:0 0 1em}.wp-block-table td,.wp-block-table th{word-break:normal}.wp-block-table :where(figcaption){color:#555;font-size:13px;text-align:center}.is-dark-theme .wp-block-table :where(figcaption){color:#ffffffa6}.wp-block-video :where(figcaption){color:#555;font-size:13px;text-align:center}.is-dark-theme .wp-block-video :where(figcaption){color:#ffffffa6}.wp-block-video{margin:0 0 1em}:root :where(.wp-block-template-part.has-background){margin-bottom:0;margin-top:0;padding:1.25em 2.375em}
35</style>
36<style id='classic-theme-styles-inline-css' type='text/css'>
37/*! This file is auto-generated */
38.wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none}
39</style>
40<style id='global-styles-inline-css' type='text/css'>
41:root{--wp--preset--aspect-ratio--square: 1;--wp--preset--aspect-ratio--4-3: 4/3;--wp--preset--aspect-ratio--3-4: 3/4;--wp--preset--aspect-ratio--3-2: 3/2;--wp--preset--aspect-ratio--2-3: 2/3;--wp--preset--aspect-ratio--16-9: 16/9;--wp--preset--aspect-ratio--9-16: 9/16;--wp--preset--color--black: #000000;--wp--preset--color--cyan-bluish-gray: #abb8c3;--wp--preset--color--white: #ffffff;--wp--preset--color--pale-pink: #f78da7;--wp--preset--color--vivid-red: #cf2e2e;--wp--preset--color--luminous-vivid-orange: #ff6900;--wp--preset--color--luminous-vivid-amber: #fcb900;--wp--preset--color--light-green-cyan: #7bdcb5;--wp--preset--color--vivid-green-cyan: #00d084;--wp--preset--color--pale-cyan-blue: #8ed1fc;--wp--preset--color--vivid-cyan-blue: #0693e3;--wp--preset--color--vivid-purple: #9b51e0;--wp--preset--gradient--vivid-cyan-blue-to-vivid-purple: linear-gradient(135deg,rgba(6,147,227,1) 0%,rgb(155,81,224) 100%);--wp--preset--gradient--light-green-cyan-to-vivid-green-cyan: linear-gradient(135deg,rgb(122,220,180) 0%,rgb(0,208,130) 100%);--wp--preset--gradient--luminous-vivid-amber-to-luminous-vivid-orange: linear-gradient(135deg,rgba(252,185,
410,1) 0%,rgba(255,105,0,1) 100%);--wp--preset--gradient--luminous-vivid-orange-to-vivid-red: linear-gradient(135deg,rgba(255,105,0,1) 0%,rgb(207,46,46) 100%);--wp--preset--gradient--very-light-gray-to-cyan-bluish-gray: linear-gradient(135deg,rgb(238,238,238) 0%,rgb(169,184,195) 100%);--wp--preset--gradient--cool-to-warm-spectrum: linear-gradient(135deg,rgb(74,234,220) 0%,rgb(151,120,209) 20%,rgb(207,42,186) 40%,rgb(238,44,130) 60%,rgb(251,105,98) 80%,rgb(254,248,76) 100%);--wp--preset--gradient--blush-light-purple: linear-gradient(135deg,rgb(255,206,236) 0%,rgb(152,150,240) 100%);--wp--preset--gradient--blush-bordeaux: linear-gradient(135deg,rgb(254,205,165) 0%,rgb(254,45,45) 50%,rgb(107,0,62) 100%);--wp--preset--gradient--luminous-dusk: linear-gradient(135deg,rgb(255,203,112) 0%,rgb(199,81,192) 50%,rgb(65,88,208) 100%);--wp--preset--gradient--pale-ocean: linear-gradient(135deg,rgb(255,245,203) 0%,rgb(182,227,212) 50%,rgb(51,167,181) 100%);--wp--preset--gradient--electric-grass: linear-gradient(135deg,rgb(202,248,128) 0%,rgb(113,206,126) 100%);--wp--preset--gradient--midnight: linear-gradient(135deg,rgb(2,3,129) 0%,rgb(40,116,252) 100%);--wp--preset--font-size--small: 13px;--wp--preset--font-size--medium: 20px;--wp--preset--font-size--large: 36px;--wp--preset--font-size--x-large: 42px;--wp--preset--spacing--20: 0.44rem;--wp--preset--spacing--30: 0.67rem;--wp--preset--spacing--40: 1rem;--wp--preset--spacing--50: 1.5rem;--wp--preset--spacing--60: 2.25rem;--wp--preset--spacing--70: 3.38rem;--wp--preset--spacing--80: 5.06rem;--wp--preset--shadow--natural: 6px 6px 9px rgba(0, 0, 0, 0.2);--wp--preset--shadow--deep: 12px 12px 50px rgba(0, 0, 0, 0.4);--wp--preset--shadow--sharp: 6px 6px 0px rgba(0, 0, 0, 0.2);--wp--preset--shadow--outlined: 6px 6px 0px -3px rgba(255, 255, 255, 1), 6px 6px rgba(0, 0, 0, 1);--wp--preset--shadow--crisp: 6px 6px 0px rgba(0, 0, 0, 1);}:where(.is-layout-flex){gap: 0.5em;}:where(.is-layout-grid){gap: 0.5em;}body .is-layout-flex{display: flex;}.is-layout-flex{flex-wrap: wrap;align-items: center;}.is-layout-flex > :is(*, div){margin: 0;}body .is-layout-grid{display: grid;}.is-layout-grid > :is(*, div){margin: 0;}:where(.wp-block-columns.is-layout-flex){gap: 2em;}:where(.wp-block-columns.is-layout-grid){gap: 2em;}:where(.wp-block-post-template.is-layout-flex){gap: 1.25em;}:where(.wp-block-post-template.is-layout-grid){gap: 1.25em;}.has-black-color{color: var(--wp--preset--color--black) !important;}.has-cyan-bluish-gray-color{color: var(--wp--preset--color--cyan-bluish-gray) !important;}.has-white-color{color: var(--wp--preset--color--white) !important;}.has-pale-pink-color{color: var(--wp--preset--color--pale-pink) !important;}.has-vivid-red-color{color: var(--wp--preset--color--vivid-red) !important;}.has-luminous-vivid-orange-color{color: var(--wp--preset--color--luminous-vivid-orange) !important;}.has-luminous-vivid-amber-color{color: var(--wp--preset--color--luminous-vivid-amber) !important;}.has-light-green-cyan-color{color: var(--wp--preset--color--light-green-cyan) !important;}.has-vivid-green-cyan-color{color: var(--wp--preset--color--vivid-green-cyan) !important;}.has-pale-cyan-blue-color{color: var(--wp--preset--color--pale-cyan-blue) !important;}.has-vivid-cyan-blue-color{color: var(--wp--preset--color--vivid-cyan-blue) !important;}.has-vivid-purple-color{color: var(--wp--preset--color--vivid-purple) !important;}.has-black-background-color{background-color: var(--wp--preset--color--black) !important;}.has-cyan-bluish-gray-background-color{background-color: var(--wp--preset--color--cyan-bluish-gray) !important;}.has-white-background-color{background-color: var(--wp--preset--color--white) !important;}.has-pale-pink-background-color{background-color: var(--wp--preset--color--pale-pink) !important;}.has-vivid-red-background-color{background-color: var(--wp--preset--color--vivid-red) !important;}.has-luminous-vivid-orange-background-color{background-color: var(--wp--preset--color--luminous-vivid-orange) !important;}.has-luminous-vivid-amber-background-color{background-color: var(--wp--preset--color--luminous-vivid-amber) !important;}.has-light-green-cyan-background-color{background-color: var(--wp--preset--color--light-green-cyan) !important;}.has-vivid-green-cyan-background-color{background-color: var(--wp--preset--color--vivid-green-cyan) !important;}.has-pale-cyan-blue-background-color{background-color: var(--wp--preset--color--pale-cyan-blue) !important;}.has-vivid-cyan-blue-background-color{background-color: var(--wp--preset--color--vivid-cyan-blue) !important;}.has-vivid-purple-background-color{background-color: var(--wp--preset--color--vivid-purple) !important;}.has-black-border-color{border-color: var(--wp--preset--color--black) !important;}.has-cyan-bluish-gray-border-color{border-color: var(--wp--preset--color--cyan-bluish-gray) !important;}.has-white-border-color{border-color: var(--wp--preset--color--white) !important;}.has-pale-pink-border-color{border-color: var(--wp--preset--color--pale-pink) !important;}.has-vivid-red-border-color{border-color: var(--wp--preset--color--vivid-red) !important;}.has-luminous-vivid-orange-border-color{border-color: var(--wp--preset--color--luminous-vivid-orange) !important;}.has-luminous-vivid-amber-border-color{border-color: var(--wp--preset--color--luminous-vivid-amber) !important;}.has-light-green-cyan-border-color{border-color: var(--wp--preset--color--light-green-cyan) !important;}.has-vivid-green-cyan-border-color{border-color: var(--wp--preset--color--vivid-green-cyan) !important;}.has-pale-cyan-blue-border-color{border-color: var(--wp--preset--color--pale-cyan-blue) !important;}.has-vivid-cyan-blue-border-color{border-color: var(--wp--preset--color--vivid-cyan-blue) !important;}.has-vivid-purple-border-color{border-color: var(--wp--preset--color--vivid-purple) !important;}.has-vivid-cyan-blue-to-vivid-purple-gradient-background{background: var(--wp--preset--gradient--vivid-cyan-blue-to-vivid-purple) !important;}.has-light-green-cyan-to-vivid-green-cyan-gradient-background{background: var(--wp--preset--gradient--light-green-cyan-to-vivid-green-cyan) !important;}.has-luminous-vivid-amber-to-luminous-vivid-orange-gradient-background{background: var(--wp--preset--gradient--luminous-vivid-amber-to-luminous-vivid-orange) !important;}.has-luminous-vivid-orange-to-vivid-red-gradient-background{background: var(--wp--preset--gradient--luminous-vivid-orange-to-vivid-red) !important;}
41.has-very-light-gray-to-cyan-bluish-gray-gradient-background{background: var(--wp--preset--gradient--very-light-gray-to-cyan-bluish-gray) !important;}.has-cool-to-warm-spectrum-gradient-background{background: var(--wp--preset--gradient--cool-to-warm-spectrum) !important;}.has-blush-light-purple-gradient-background{background: var(--wp--preset--gradient--blush-light-purple) !important;}.has-blush-bordeaux-gradient-background{background: var(--wp--preset--gradient--blush-bordeaux) !important;}.has-luminous-dusk-gradient-background{background: var(--wp--preset--gradient--luminous-dusk) !important;}.has-pale-ocean-gradient-background{background: var(--wp--preset--gradient--pale-ocean) !important;}.has-electric-grass-gradient-background{background: var(--wp--preset--gradient--electric-grass) !important;}.has-midnight-gradient-background{background: var(--wp--preset--gradient--midnight) !important;}.has-small-font-size{font-size: var(--wp--preset--font-size--small) !important;}.has-medium-font-size{font-size: var(--wp--preset--font-size--medium) !important;}.has-large-font-size{font-size: var(--wp--preset--font-size--large) !important;}.has-x-large-font-size{font-size: var(--wp--preset--font-size--x-large) !important;}
42:where(.wp-block-post-template.is-layout-flex){gap: 1.25em;}:where(.wp-block-post-template.is-layout-grid){gap: 1.25em;}
43:where(.wp-block-columns.is-layout-flex){gap: 2em;}:where(.wp-block-columns.is-layout-grid){gap: 2em;}
44:root :where(.wp-block-pullquote){font-size: 1.5em;line-height: 1.6;}
45</style>
46<link rel='stylesheet' id='graceful-style-css' href='http://www.kevinhouston.net/blog/wp-content/themes/graceful/style.css?ver=6.6.9' type='text/css' media='all' />
47<style id='graceful-style-inline-css' type='text/css'>
48 .wrapped-content { max-width: 1160px; } .sidebar-slide-menu { width: 340px; left: -340px; padding: 85px 35px 0px; } .sidebar-left, .sidebar-right { width: 307px; } [data-layout*="rightsidebar"] .content-wrap, [data-layout*="leftsidebar"] .content-wrap { width: calc(100% - 307px); width: -webkit-calc(100% - 307px); } [data-layout*="leftrightsidebar"] .content-wrap { width: calc(100% - 614px); width: -webkit-calc(100% - 614px); } [data-layout*="fullwidth"] .content-wrap { width: 100%; } #top-navigation > div, #main-navigation > div, #graceful-post-slider.wrapped-content, #special-links, .main-content, .site-footer-wrap { padding-left: 40px; padding-right: 40px; } body { background-color: #ffffff; } .graceful-loading-wrap { background-color: #ffffff; } .site-branding a { background-color: transparent !important; } .site-branding a { color: #0166bf; background: #ffffff; } .entry-header { background-color: #ffffff; } #special-links h4 { background-color: rgba(241,241,241, 0.85); color: #000000; } #main-navigation a, #main-navigation i, #main-navigation #s { color: #000000; } .main-navigation-sidebar span, .sidebar-slide-menu-close-btn span { background-color: #000000; } #main-navigation a:hover, #main-navigation i:hover, #main-navigation li.current-menu-item > a, #main-navigation li.current-menu-ancestor > a, #main-navigation .sub-menu li.current-menu-item > a, #main-navigation .sub-menu li.current-menu-ancestor> a { color: #0066bf; } .main-navigation-sidebar:hover span { background-color: #0066bf; } #site-menu .sub-menu, #site-menu .sub-menu a { background-color: #f1f1f1; border-color: rgba(0,0,0, 0.1); } #main-navigation #s { background-color: #f1f1f1; } #main-navigation #s::-webkit-input-placeholder { /* Chrome/Opera/Safari */ color: rgba(0,0,0, 0.7); } #main-navigation #s::-moz-placeholder { /* Firefox 19+ */ color: rgba(0,0,0, 0.7); } #main-navigation #s:-ms-input-placeholder { /* IE 10+ */ color: rgba(0,0,0, 0.7); } #main-navigation #s:-moz-placeholder { /* Firefox 18- */ color: rgba(0,0,0, 0.7); } /* Background Color */ .sidebar-slide-menu, #special-links, .main-content, #graceful-post-slider, #primary select, #primary input, #primary textarea { background-color: #ffffff; } /* Text Color */ #primary, #primary select, #primary input, #primary textarea, #primary .post-author a, #primary .graceful-widget a, #primary .comment-author { color: #010101; } /* Title Color */ #primary h1 a, #primary h1, #primary h2, #primary h3, #primary h4, #primary h5, #primary h6, .post-page-content > p:first-child:first-letter, #primary .author-info h4 a, #primary .related-posts h4 a, #primary .content-pagination .previous-page a, #primary .content-pagination .next-page a, blockquote, #primary .post-share a { color: #030303; } #primary h1 a:hover { color: rgba(3,3,3, 0.75); } /* Meta Tags */ #primary .post-date, #primary .post-comments, #primary .post-author, #primary .related-post-date, #primary .comment-meta a, #primary .author-share a, #primary .post-tags a, #primary .tagcloud a, .widget_categories li, .widget_archive li, .a
48hse-subscribe-box p, .rpwwt-post-author, .rpwwt-post-categories, .rpwwt-post-date, .rpwwt-post-comments-number { color: #a1a1a1; } #primary input::-webkit-input-placeholder { /* Chrome/Opera/Safari */ color: #a1a1a1; } #primary input::-moz-placeholder { /* Firefox 19+ */ color: #a1a1a1; } #primary input:-ms-input-placeholder { /* IE 10+ */ color: #a1a1a1; } #primary input:-moz-placeholder { /* Firefox 18- */ color: #a1a1a1; } /* Brand Colors */ aside a, #primary a, .post-categories { color: #0066bf; } .ps-container > .ps-scrollbar-y-rail > .ps-scrollbar-y { background: #0066bf; } #primary a:hover { color: rgba(0,102,191, 0.8); } blockquote { border-color: #0066bf; } /* Selection Color */ ::-moz-selection { color: #ffffff; background: #0066bf; } ::selection { color: #ffffff; background: #0066bf; } /* Border Colors */ #primary .post-footer, #primary .author-info, #primary .entry-comments, #primary .graceful-widget li, #primary #wp-calendar, #primary #wp-calendar caption, #primary #wp-calendar tbody td, #primary .widget_nav_menu li a, #primary .tagcloud a, #primary select, #primary input, #primary textarea, .widget-title h2:before, .widget-title h2:after, .post-tags a, .gallery-caption, .wp-caption-text, table tr, table th, table td, pre { border-color: #e8e8e8; } /* Related-posts */ #primary .related-posts { border-bottom: 1px solid; border-top: 1px solid; padding: 27px 0 33px; border-color: #e8e8e8; } .related-posts h3 { font-family: 'Montserrat', sans-serif; font-size: 14px; font-weight: 600; letter-spacing: 2px; line-height: 1; margin-bottom: 19px; text-align: center; text-transform: uppercase; } .related-posts h4 { margin-top: 8px; } .related-posts h4 a { font-size: 18px; letter-spacing: 0.5px; } .related-posts section { float: left; margin-right: 23px; width: calc((100% - (2 * 23px)) / 3); width: -webkit-calc((100% - (2 * 23px)) / 3); } .related-posts section:last-of-type { margin-right: 0 !important; } .related-posts section > a { display: block; height: 130px; overflow: hidden; } .related-post-date { font-size: 11px; } hr { background-color: #e8e8e8; } /* Button Colors */ .widget_search i, .widget_search #searchsubmit, .post-navigation i, #primary .submit, #primary .content-pagination.numeric a, #primary .content-pagination.load-more a, #primary .graceful-subscribe-box input[type="submit"], #primary .widget_wysija input[type="submit"], #primary .post-password-form input[type="submit"], #primary .wpcf7 [type="submit"] { color: #ffffff; background-color: #555555; } .post-navigation i:hover, #primary .submit:hover, #primary .content-pagination.numeric a:hover, #primary .content-pagination.numeric span, #primary .content-pagination.load-more a:hover, #primary .graceful-subscribe-box input[type="submit"]:hover, #primary .widget_wysija input[type="submit"]:hover, #primary .post-password-form input[type="submit"]:hover, #primary .wpcf7 [type="submit"]:hover { color: #ffffff; background-color: #0066bf; } /* Image Overlay Color */ .image-overlay, #infinite-scrolling, #primary h4.image-overlay { color: #ffffff; background-color: rgba(0,0,0, 0.3); } .image-overlay a, .graceful-post-slider .prev-arrow, .graceful-post-slider .next-arrow, #primary .image-overlay a, #graceful-post-slider .slick-arrow, #graceful-post-slider .slider-dots { color: #ffffff; } .slide-caption { background: rgba(255,255,255, 0.95); } #graceful-post-slider .slick-active { background: #ffffff; } #site-footer, #site-footer select, #site-footer input, #site-footer textarea { background-color: #f6f6f6; color: #333333; } #site-footer, #site-footer a, #site-footer select, #site-footer input, #site-footer textarea { color: #333333; } #site-footer #s::-webkit-input-placeholder { /* Chrome/Opera/Safari */ color: #333333; } #site-footer #s::-moz-placeholder { /* Firefox 19+ */ color: #333333; } #site-footer #s:-ms-input-placeholder { /* IE 10+ */ color: #333333; } #site-footer #s:-moz-placeholder { /* Firefox 18- */ color: #333333; } /* Footer Title Color */ #site-footer h1, #site-footer h2, #site-footer h3, #site-footer h4, #site-footer h5, #site-footer h6 { color: #111111; } #site-footer a:hover { color: #0066bf; } /* Footer Border Color*/ #site-footer a, #site-footer .graceful-widget li, #site-footer #wp-calendar, #site-footer #wp-calendar caption, #site-footer #wp-calendar tbody td, #site-footer .widget_nav_menu li a, #site-footer select, #site-footer input, #site-footer textarea, #site-footer .widget-title h2:before, #site-footer .widget-title h2:after, .footer-widgets { border-color: #e
480dbdb; } #site-footer hr { background-color: #e0dbdb; } .entry-header { background-image:url(); } .logo-img { max-width: 400px; } #main-navigation { text-align: left; } .main-navigation-sidebar { float: left; margin-right: 15px; } .main-navigation-search { float: right; margin-left: 15px; } .site-menu-wrapper { margin-right: 100px; } .main-navigation-sidebar { float: left; margin-right: 15px; } .main-navigation-search { float: right; margin-left: 15px; } .site-menu-wrapper { margin-right: 110px; } #graceful-post-slider { padding-top: 40px; } #graceful-post-slider .owl-nav button { display: inline-block; } #graceful-post-slider .owl-nav { background-color: #f3f3f3; height: 80px; } #graceful-post-slider .owl-stage-outer:after { display: block; } .content-column > li { margin-bottom: 100px; } [data-layout*="rightsidebar"] .sidebar-right { padding-left: 37px; } [data-layout*="leftsidebar"] .sidebar-left { padding-right: 37px; } [data-layout*="leftrightsidebar"] .sidebar-right { padding-left: 37px; } [data-layout*="leftrightsidebar"] .sidebar-left { padding-right: 37px; } .footer-widgets > .graceful-widget { width: 30%; margin-right: 5%; } .footer-widgets > .graceful-widget:nth-child(3n+3) { margin-right: 0; } .footer-widgets > .graceful-widget:nth-child(3n+4) { clear: both; } .footer-copyright { float: right; } .footer-socials { float: left; } .graceful-loading-wrap { height: 100%; left: 0; position: fixed; top: 0; width: 100%; z-index: 100000; } .graceful-loading-wrap > div { left: 50%; position: absolute; top: 50%; -webkit-transform: translate(-50%, -50%); -ms-transform: translate(-50%, -50%); transform: translate(-50%, -50%); } .cssload-container{width:100%;height:36px;text-align:center}.cssload-speeding-wheel{width:36px;height:36px;margin:0 auto;border:2px solid #000000; border-radius:50%;border-left-color:transparent;border-right-color:transparent;animation:cssload-spin 575ms infinite linear;-o-animation:cssload-spin 575ms infinite linear;-ms-animation:cssload-spin 575ms infinite linear;-webkit-animation:cssload-spin 575ms infinite linear;-moz-animation:cssload-spin 575ms infinite linear}@keyframes cssload-spin{100%{transform:rotate(360deg);transform:rotate(360deg)}}@-o-keyframes cssload-spin{100%{-o-transform:rotate(360deg);transform:rotate(360deg)}}@-ms-keyframes cssload-spin{100%{-ms-transform:rotate(360deg);transform:rotate(360deg)}}@-webkit-keyframes cssload-spin{100%{-webkit-transform:rotate(360deg);transform:rotate(360deg)}}@-moz-keyframes cssload-spin{100%{-moz-transform:rotate(360deg);transform:rotate(360deg)}} 
49</style>
50<link rel='stylesheet' id='graceful-minimal-style-css' href='http://www.kevinhouston.net/blog/wp-content/themes/graceful-minimal/style.css?ver=1.0.0' type='text/css' media='all' />
51<link rel='stylesheet' id='minimalist-stories-fonts-css' href='http://www.kevinhouston.net/blog/wp-content/fonts/ab7d42133ebad65dc2d936d78801d1f0.css?ver=1.0' type='text/css' media='all' />
52<link rel='stylesheet' id='graceful-fontawesome-css' href='http://www.kevinhouston.net/blog/wp-content/themes/graceful/assets/css/font-awesome.css?ver=6.6.9' type='text/css' media='all' />
53<link rel='stylesheet' id='graceful-google-fonts-css' href='http://www.kevinhouston.net/blog/wp-content/themes/graceful/assets/css/google-fonts.css?ver=6.6.9' type='text/css' media='all' />
54<link rel='stylesheet' id='graceful-woocommerce-css' href='http://www.kevinhouston.net/blog/wp-content/themes/graceful/assets/css/woocommerce.css?ver=6.6.9' type='text/css' media='all' />
55<script type="text/javascript" src="http://www.kevinhouston.net/blog/wp-includes/js/jquery/jquery.min.js?ver=3.7.1" id="jquery-core-js"></script>
vendor: 1 bytes, line 55
55
56<script type="text/javascript" src="http://www.kevinhouston.net/blog/wp-includes/js/jquery/jquery-migrate.min.js?ver=3.4.1" id="jquery-migrate-js"></script>
56
57<link rel="https://api.w.org/" href="https://www.kevinhouston.net/blog/wp-json/" /><link rel="EditURI" type="application/rsd+xml" title="RSD" href="https://www.kevinhouston.net/blog/xmlrpc.php?rsd" />
58<meta name="generator" content="WordPress 6.6.9" />
59<link rel='shortlink' href='http://wp.me/16v0k' />
60<style type="text/css">
61/* <![CDATA[ */
62img.latex { vertical-align: middle; border: none; }
63/* ]]> */
64</style>
65</head>
66<body class="home blog wp-embed-responsive">
67    
68	
69	
70	<a class="skip-link screen-reader-text" href="#primary">Skip to content</a>	
71
72	<div id="site-container">
73		<div id="site-header" >
74			<div class="entry-header">
75		<div class="graceful-wrap-outer">
76		<div class="graceful-wrap-inner">
77			<div class="site-branding">
78							<a href="https://www.kevinhouston.net/blog/">Kevin Houston</a>
79			
80							<br>
81				<p class="site-description">Thinking mathematically&#8230;</p>
82						</div>
83		</div>
84		</div>
85	</div><div id="main-navigation" class="clear-fix" data-fixed="1">
86	<div class="wrapped-content">
87		<div class="navigation-search-overlay">
88		</div>
89		
90		
91		<!-- Menu -->
92		<button class="responsive-menu-btn">
93			<i class="fa fa-chevron-down"></i>
94			<i class="fa fa-times" style="display: none;"></i>
95		</button>
96
97		
98		
99	    <div class="navigation-socials">
100	        	            	        	            	        	            	        	            	        	    </div>
101
102    		
103		<!-- Search in main navigation -->		
104				<div class="main-navigation-search">
105			<button class="navigation-search-button open-graceful-search">
106				<i class="fa fa-search"></i>
107				<i class="fa fa-times"></i>
108			</button>
109			<div class="graceful-search" role="graceful-search" aria-labelledby="graceful-search-title" aria-describedby="graceful-search-description" aria-hidden="true">
110				<form role="search" method="get" id="searchform" class="searchform" action="https://www.kevinhouston.net/blog/">
111				<div>
112					<label class="screen-reader-text" for="s">Search for:</label>
113					<input type="text" value="" name="s" id="s" />
114					<input type="submit" id="searchsubmit" value="Search" />
115				</div>
116			</form>				<button type="button" aria-label="Close Navigation" class="close-graceful-search"> <i class="fa fa-times"></i> </button>
117			</div>
118			<div class="graceful-search-overlay" tabindex="-1" aria-hidden="true"></div>
119		</div>
120		
121	</div>
122</div><!-- #main-navigation -->
123		</div><!-- site-header close -->
124
125		<!-- Page Content -->
126		<main id="primary" class="site-main">
127				<div class="main-content clear-fix wrapped-content" data-layout="col1-rightsidebar" data-sidebar-sticky="1">
128<div class="content-wrap">
129		<ul class="content-column">
130					<li>
131				<article id="post-4500" class="content-post post-4500 post type-post status-publish format-standard hentry category-mathematics-education">
132					<div class="site-images">
133											</div>
134
135					<header class="post-header">
136						<div class="post-header-inner">
137															<div class="post-categories">
138									<a href="https://www.kevinhouston.net/blog/category/mathematics-education/" rel="category tag">Mathematics education</a>								</div>
139							
140							<h2 class="post-title">
141								<a href="https://www.kevinhouston.net/blog/2021/01/lessons-learned-from-covid-19-teaching/">Lessons Learned From Covid-19 Teaching</a>
142							</h2>
143
144							<div class="post-meta clear-fix">
145																	<span class="post-date">January 5, 2021</span>
146								
147								<strong class="post-title-author">
148									 - By&nbsp;<a href="https://www.kevinhouston.net/blog/author/admin/" title="Posts by Kevin Houston" rel="author">Kevin Houston</a>								</strong>
149							</div>
150						</div>
151					</header>
152
153											<div class="post-page-content">
154							<p>What can I say? 2020, Covid, unprecedented, etc. You already know this. Well, since I&#8217;m co-organising a Teaching and Learning Mathematics Online (TALMO) workshop today on lessons learned following the sudden switch to online teaching I decided to write down some of my lessons learned. The TALMO meeting can be found at Tackling Term 2: Top Tips from Term 1. Last term, apart from a single hour right at the start, my teaching was online. As expected it didn&#8217;t go perfectly. Actually, some of it went quite badly and I&#8217;ll talk about that on another day. For the moment I&#8217;ll&hellip;</p>						</div>
155					
156					<footer class="post-footer">
157											<div class="continue-read">
158							<a href="https://www.kevinhouston.net/blog/2021/01/lessons-learned-from-covid-19-teaching/">Continue Reading</a>
159						</div>
160										</footer>
161
162					
163				</article>
164			</li>
165
166					<li>
167				<article id="post-4446" class="content-post post-4446 post type-post status-publish format-standard hentry category-mathematics-education tag-covid-19 tag-mathematics-assessment tag-open-book-exam tag-take-home-exam">
168					<div class="site-images">
169											</div>
170
171					<header class="post-header">
172						<div class="post-header-inner">
173															<div class="post-categories">
174									<a href="https://www.kevinhouston.net/blog/category/mathematics-education/" rel="category tag">Mathematics education</a>								</div>
175							
176							<h2 class="post-title">
177								<a href="https://www.kevinhouston.net/blog/2020/03/mathematics-take-away-open-book-assessment/">Mathematics Take Away Open Book Assessment</a>
178							</h2>
179
180							<div class="post-meta clear-fix">
181																	<span class="post-date">March 20, 2020</span>
182								
183								<strong class="post-title-author">
184									 - By&nbsp;<a href="https://www.kevinhouston.net/blog/author/admin/" title="Posts by Kevin Houston" rel="author">Kevin Houston</a>								</strong>
185							</div>
186						</div>
187					</header>
188
189											<div class="post-page-content">
190							<p>With the current Covid-19 crisis many Higher Education Institutions (HEIs) are moving to take away exams which by their nature are open book exams. Many mathematicians do not have experience of take home open book assessments and this post is intended to help deal with this. This has been put together quickly and is intended to be practical rather than theoretical. I hope you find it of use. I 
190will update when I can so if you have any suitable links or ideas, then please leave a comment. Principles Throughout the next few months, students and staff will be sick,&hellip;</p>						</div>
191					
192					<footer class="post-footer">
193											<div class="continue-read">
194							<a href="https://www.kevinhouston.net/blog/2020/03/mathematics-take-away-open-book-assessment/">Continue Reading</a>
195						</div>
196										</footer>
197
198					
199				</article>
200			</li>
201
202					<li>
203				<article id="post-4441" class="content-post post-4441 post type-post status-publish format-standard hentry category-how-to-think-like-a-mathematician category-mathematical-thinking category-mathematics-education">
204					<div class="site-images">
205											</div>
206
207					<header class="post-header">
208						<div class="post-header-inner">
209															<div class="post-categories">
210									<a href="https://www.kevinhouston.net/blog/category/how-to-think-like-a-mathematician/" rel="category tag">How To Think Like A Mathematician</a>&nbsp;-&nbsp;<a href="https://www.kevinhouston.net/blog/category/mathematical-thinking/" rel="category tag">Mathematical thinking</a>&nbsp;-&nbsp;<a href="https://www.kevinhouston.net/blog/category/mathematics-education/" rel="category tag">Mathematics education</a>								</div>
211							
212							<h2 class="post-title">
213								<a href="https://www.kevinhouston.net/blog/2019/04/e-assessment/">E-assessment</a>
214							</h2>
215
216							<div class="post-meta clear-fix">
217																	<span class="post-date">April 10, 2019</span>
218								
219								<strong class="post-title-author">
220									 - By&nbsp;<a href="https://www.kevinhouston.net/blog/author/admin/" title="Posts by Kevin Houston" rel="author">Kevin Houston</a>								</strong>
221							</div>
222						</div>
223					</header>
224
225											<div class="post-page-content">
226							<p>I&#8217;ve been attending a conference for the last few days and so didn&#8217;t have much time to write a post. I did learn about the e-assessment packages Stack and Numbas. I will definitely be trying these in the future.</p>						</div>
227					
228					<footer class="post-footer">
229											<div class="continue-read">
230							<a href="https://www.kevinhouston.net/blog/2019/04/e-assessment/">Continue Reading</a>
231						</div>
232										</footer>
233
234					
235				</article>
236			</li>
237
238					<li>
239				<article id="post-4438" class="content-post post-4438 post type-post status-publish format-standard hentry category-how-to-think-like-a-mathematician category-mathematical-thinking category-mathematics-education">
240					<div class="site-images">
241											</div>
242
243					<header class="post-header">
244						<div class="post-header-inner">
245															<div class="post-categories">
246									<a href="https://www.kevinhouston.net/blog/category/how-to-think-like-a-mathematician/" rel="category tag">How To Think Like A Mathematician</a>&nbsp;-&nbsp;<a href="https://www.kevinhouston.net/blog/category/mathematical-thinking/" rel="category tag">Mathematical thinking</a>&nbsp;-&nbsp;<a href="https://www.kevinhouston.net/blog/category/mathematics-education/" rel="category tag">Mathematics education</a>								</div>
247							
248							<h2 class="post-title">
249								<a href="https://www.kevinhouston.net/blog/2019/04/proof-from-the-particular-to-the-general/">Proof: From the particular to the general</a>
250							</h2>
251
252							<div class="post-meta clear-fix">
253																	<span class="post-date">April 9, 2019</span>
254								
255								<strong class="post-title-author">
256									 - By&nbsp;<a href="https://www.kevinhouston.net/blog/author/admin/" title="Posts by Kevin Houston" rel="author">Kevin Houston</a>								</strong>
257							</div>
258						</div>
259					</header>
260
261											<div class="post-page-content">
262							<p>A common technique in teaching mathematics is to go from the particular to the general. We can look at a few examples and then state and prove the general result. We can do this for proofs as well. Instead of giving students a proof of a statement, give them the proof for a specific example of the statement and ask them to prove the general from that. A classic example of this is to prove the irrationality of and then that of . Once the common features have been determined the proof for irrationality of for prime is (hopefully) straightforward.&hellip;</p>						</div>
263					
264					<footer class="post-footer">
265											<div class="continue-read">
266							<a href="https://www.kevinhouston.net/blog/2019/04/proof-from-the-particular-to-the-general/">Continue Reading</a>
267						</div>
268										</footer>
269
270					
271				</article>
272			</li>
273
274					<li>
275				<article id="post-4434" class="content-post post-4434 post type-post status-publish format-standard hentry category-how-to-think-like-a-mathematician category-mathematical-thinking category-mathematics-education">
276					<div class="site-images">
277											</div>
278
279					<header class="post-header">
280						<div class="post-header-inner">
281															<div class="post-categories">
282									<a href="https://www.kevinhouston.net/blog/category/how-to-think-like-a-mathematician/" rel="category tag">How To Think Like A Mathematician</a>&nbsp;-&nbsp;<a href="https://www.kevinhouston.net/blog/category/mathematical-thinking/" rel="category tag">Mathematical thinking</a>&nbsp;-&nbsp;<a href="https://www.kevinhouston.net/blog/category/mathematics-education/" rel="category tag">Mathematics education</a>								</div>
283							
284							<h2 class="post-title">
285								<a href="https://www.kevinhouston.net/blog/2019/04/marks-for-writing/">Marks for writing</a>
286							</h2>
287
288							<div class="post-meta clear-fix">
289																	<span class="post-date">April 8, 2019</span>
290								
291								<strong class="post-title-author">
292									 - By&nbsp;<a href="https://www.kevinhouston.net/blog/author/admin/" title="Posts by Kevin Houston" rel="author">Kevin Houston</a>								</strong>
293							</div>
294						</div>
295					</header>
296
297											<div class="post-page-content">
298							<p>Writing mathematics clearly is a crucial part of a student&#8217;s education. Too often students begin higher education with the misconception that writing mathematics merely involves putting down a sequence of symbols without paying too much attention as to whether they make sense to the reader. As long as the answer is there in some form and underlined, that&#8217;s ok, the thinking goes. Since the marker can see that the answer is there, this may be almost acceptable for problems such as finding the derivative of some product. But it does not work for writing proofs where a logical and coherent&hellip;</p>						</div>
299					
300					<footer class="post-footer">
301											<div class="continue-read">
302							<a href="https://www.kevinhouston.net/blog/2019/04/marks-for-writing/">Continue Reading</a>
303						</div>
304										</footer>
305
306					
307				</article>
308			</li>
309
310			</ul>
311	
312<nav class="content-pagination clear-fix default"
313	data-max-pages="45"
314	data-loading="Loading...">
315
316				<div class="previous-page">
317				<a href="https://www.kevinhouston.net/blog/page/2/" ><i class="fa fa-long-arrow-left"></i>&nbsp;Older Posts</a>			</div>
318		
319</nav>
320</div><!-- content-wrap -->
321<div class="sidebar-right-wrap">
322	<aside class="sidebar-right">
323	    	        <section id="recent-posts-5" class="graceful-widget widget_recent_entries"><h2>Recent Posts</h2>            <ul>
324                            <li class="graceful-recent-image-box">
325                    <div class="graceful-small-image-box" style="background-image: url( '' );">
326                    </div>
327                                    		<a href="https://www.kevinhouston.net/blog/2021/01/lessons-learned-from-covid-19-teaching/">Lessons Learned From Covid-19 Teaching</a>
328                </li>
329                            <li class="graceful-recent-image-box">
330                    <div class="graceful-small-image-box" style="background-image: url( '' );">
331                    </div>
332                                    		<a href="https://www.kevinhouston.net/blog/2020/03/mathematics-take-away-open-book-assessment/">Mathematics Take Away Open Book Assessment</a>
333                </li>
334                            <li class="graceful-recent-image-box">
335                    <div class="graceful-small-image-box" style="background-image: url( '' );">
336                    </div>
337                                    		<a href="https://www.kevinhouston.net/blog/2019/04/e-assessment/">E-assessment</a>
338                </li>
339                            <li class="graceful-recent-image-box">
340                    <div class="graceful-small-image-box" style="background-image: url( '' );">
341                    </div>
342                                    		<a href="https://www.kevinhouston.net/blog/2019/04/proof-from-the-particular-to-the-general/">Proof: From the particular to the general</a>
343                </li>
344                        </ul>
345            </section><section id="search-4" class="graceful-widget widget_search"><h2 class="widget-title">Search posts</h2><form role="search" method="get" id="searchform" class="searchform" action="https://www.kevinhouston.net/blog/">
346				<div>
347					<label class="screen-reader-text" for="s">Search for:</label>
348					<input type="text" value="" name="s" id="s" />
349					<input type="submit" id="searchsubmit" value="Search" />
350				</div>
351			</form></section><section id="categories-4" class="graceful-widget widget_categories"><h2 class="widget-title">Categories</h2>
352			<ul>
353					<li class="cat-item cat-item-8"><a href="https://www.kevinhouston.net/blog/category/book-review/">Book review</a> (3)
354</li>
355	<li class="cat-item cat-item-254"><a href="https://www.kevinhouston.net/blog/category/complex-analysis-2/">Complex Analysis</a> (3)
356</li>
357	<li class="cat-item cat-item-4"><a href="https://www.kevinhouston.net/blog/category/fun-mathematics/">Fun mathematics</a> (54)
358</li>
359	<li class="cat-item cat-item-12"><a href="https://www.kevinhouston.net/blog/category/history-of-mathematics/">History of Mathematics</a> (16)
360</li>
361	<li class="cat-item cat-item-16"><a href="https://www.kevinhouston.net/blog/category/how-to-think-like-a-mathematician/">How To Think Like A Mathematician</a> (48)
362</li>
363	<li class="cat-item cat-item-3"><a href="https://www.kevinhouston.net/blog/category/mathematical-thinking/">Mathematical thinking</a> (61)
364</li>
365	<li class="cat-item cat-item-9"><a href="https://www.kevinhouston.net/blog/category/mathematics-education/">Mathematics education</a> (78)
366</li>
367	<li class="cat-item cat-item-19"><a href="https://www.kevinhouston.net/blog/category/obituary/">Obituary</a> (4)
368</li>
369	<li class="cat-item cat-item-31"><a href="https://www.kevinhouston.net/blog/category/politics/">Politics</a> (9)
370</li>
371	<li class="cat-item cat-item-27"><a href="https://www.kevinhouston.net/blog/category/popularization-of-maths/">Popularization of maths</a> (53)
372</li>
373	<li class="cat-item cat-item-10"><a href="https://www.kevinhouston.net/blog/category/research/">Research</a> (12)
374</li>
375	<li class="cat-item cat-item-309"><a href="https://www.kevinhouston.net/blog/category/sequences-and-series/">Sequences and Series</a> (1)
376</li>
377	<li class="cat-item cat-item-11"><a href="https://www.kevinhouston.net/blog/category/study-techniques/">Study techniques</a> (10)
378</li>
379	<li class="cat-item cat-item-7"><a href="https://www.kevinhouston.net/blog/category/ted/">TED</a> (18)
380</li>
381	<li class="cat-item cat-item-1"><a href="https://www.kevinhouston.net/blog/category/uncategorized/">Uncategorized</a> (20)
382</li>
383	<li class="cat-item cat-item-82"><a href="https://www.kevinhouston.net/blog/category/video/">video</a> (21)
384</li>
385			</ul>
386
387			</section><section id="archives-5" class="graceful-widget widget_archive"><h2 class="widget-title">Previously&#8230;</h2>
388			<ul>
389					<li><a href='https://www.kevinhouston.net/blog/2021/01/'>January 2021</a></li>
390	<li><a href='https://www.kevinhouston.net/blog/2020/03/'>March 2020</a></li>
391	<li><a href='https://www.kevinhouston.net/blog/2019/04/'>April 2019</a></li>
392	<li><a href='https://www.kevinhouston.net/blog/2019/03/'>
392March 2019</a></li>
393	<li><a href='https://www.kevinhouston.net/blog/2018/05/'>May 2018</a></li>
394	<li><a href='https://www.kevinhouston.net/blog/2018/03/'>March 2018</a></li>
395	<li><a href='https://www.kevinhouston.net/blog/2017/10/'>October 2017</a></li>
396	<li><a href='https://www.kevinhouston.net/blog/2017/07/'>July 2017</a></li>
397	<li><a href='https://www.kevinhouston.net/blog/2016/05/'>May 2016</a></li>
398	<li><a href='https://www.kevinhouston.net/blog/2015/05/'>May 2015</a></li>
399	<li><a href='https://www.kevinhouston.net/blog/2015/04/'>April 2015</a></li>
400	<li><a href='https://www.kevinhouston.net/blog/2015/01/'>January 2015</a></li>
401	<li><a href='https://www.kevinhouston.net/blog/2014/12/'>December 2014</a></li>
402	<li><a href='https://www.kevinhouston.net/blog/2014/09/'>September 2014</a></li>
403	<li><a href='https://www.kevinhouston.net/blog/2014/07/'>July 2014</a></li>
404	<li><a href='https://www.kevinhouston.net/blog/2014/03/'>March 2014</a></li>
405	<li><a href='https://www.kevinhouston.net/blog/2014/02/'>February 2014</a></li>
406	<li><a href='https://www.kevinhouston.net/blog/2014/01/'>January 2014</a></li>
407	<li><a href='https://www.kevinhouston.net/blog/2013/12/'>December 2013</a></li>
408	<li><a href='https://www.kevinhouston.net/blog/2013/11/'>November 2013</a></li>
409	<li><a href='https://www.kevinhouston.net/blog/2013/10/'>October 2013</a></li>
410	<li><a href='https://www.kevinhouston.net/blog/2013/09/'>September 2013</a></li>
411	<li><a href='https://www.kevinhouston.net/blog/2013/08/'>August 2013</a></li>
412	<li><a href='https://www.kevinhouston.net/blog/2013/07/'>July 2013</a></li>
413	<li><a href='https://www.kevinhouston.net/blog/2013/06/'>June 2013</a></li>
414	<li><a href='https://www.kevinhouston.net/blog/2013/05/'>May 2013</a></li>
415	<li><a href='https://www.kevinhouston.net/blog/2013/04/'>April 2013</a></li>
416	<li><a href='https://www.kevinhouston.net/blog/2013/03/'>March 2013</a></li>
417	<li><a href='https://www.kevinhouston.net/blog/2013/02/'>February 2013</a></li>
418	<li><a href='https://www.kevinhouston.net/blog/2013/01/'>January 2013</a></li>
419	<li><a href='https://www.kevinhouston.net/blog/2012/12/'>December 2012</a></li>
420	<li><a href='https://www.kevinhouston.net/blog/2012/11/'>November 2012</a></li>
421	<li><a href='https://www.kevinhouston.net/blog/2012/10/'>October 2012</a></li>
422	<li><a href='https://www.kevinhouston.net/blog/2012/09/'>September 2012</a></li>
423	<li><a href='https://www.kevinhouston.net/blog/2012/08/'>August 2012</a></li>
424	<li><a href='https://www.kevinhouston.net/blog/2012/07/'>July 2012</a></li>
425	<li><a href='https://www.kevinhouston.net/blog/2012/06/'>June 2012</a></li>
426	<li><a href='https://www.kevinhouston.net/blog/2012/05/'>May 2012</a></li>
427	<li><a href='https://www.kevinhouston.net/blog/2012/04/'>April 2012</a></li>
428	<li><a href='https://www.kevinhouston.net/blog/2012/03/'>March 2012</a></li>
429	<li><a href='https://www.kevinhouston.net/blog/2012/02/'>February 2012</a></li>
430	<li><a href='https://www.kevinhouston.net/blog/2012/01/'>January 2012</a></li>
431	<li><a href='https://www.kevinhouston.net/blog/2011/12/'>December 2011</a></li>
432	<li><a href='https://www.kevinhouston.net/blog/2011/11/'>November 2011</a></li>
433	<li><a href='https://www.kevinhouston.net/blog/2011/10/'>October 2011</a></li>
434	<li><a href='https://www.kevinhouston.net/blog/2011/09/'>September 2011</a></li>
435	<li><a href='https://www.kevinhouston.net/blog/2011/08/'>August 2011</a></li>
436	<li><a href='https://www.kevinhouston.net/blog/2011/07/'>July 2011</a></li>
437	<li><a href='https://www.kevinhouston.net/blog/2011/06/'>June 2011</a></li>
438	<li><a href='https://www.kevinhouston.net/blog/2011/05/'>May 2011</a></li>
439	<li><a href='https://www.kevinhouston.net/blog/2011/04/'>April 2011</a></li>
440	<li><a href='https://www.kevinhouston.net/blog/2011/03/'>March 2011</a></li>
441	<li><a href='https://www.kevinhouston.net/blog/2011/02/'>February 2011</a></li>
442	<li><a href='https://www.kevinhouston.net/blog/2011/01/'>January 2011</a></li>
443	<li><a href='https://www.kevinhouston.net/blog/2010/12/'>December 2010</a></li>
444	<li><a href='https://www.kevinhouston.net/blog/2010/11/'>November 2010</a></li>
445	<li><a href='https://www.kevinhouston.net/blog/2010/10/'>October 2010</a></li>
446	<li><a href='https://www.kevinhouston.net/blog/2010/09/'>September 2010</a></li>
447			</ul>
448
449			</section><section id="text-3" class="graceful-widget widget_text"><h2 class="widget-title">Featured Posts</h2>			<div class="textwidget"><ul>
450<li>
451<a href="http://www.kevinhouston.net/blog/2014/09/how-to-get-a-good-degree-3-how-to-become-a-straight-a-student/">
451How to become a straight-A student</a></li>
452<li><a href="http://www.kevinhouston.net/blog/2010/09/hello-world/">10 Ways to Think Like a Mathematician</a></li>
453<li><a href=" http://www.kevinhouston.net/blog/2011/06/how-to-get-a-good-maths-degree/">How to get a good maths degree<a></li>
454<li>
455<a href="http://www.kevinhouston.net/blog/2011/03/how-not-to-get-a-good-mathematics-degree/">How not to get a good mathematics degree</a></li>
456<li><a href="http://www.kevinhouston.net/blog/2013/03/what-is-the-best-proof-of-cauchys-integral-theorem/">What is the best proof of Cauchy's Integral Theorem?</a></li>
457<li>
458<a href="http://www.kevinhouston.net/blog/2010/11/milnor-and-darcy-thompson/">Milnor and D'Arcy Thompson</a></li>
459</ul></div>
460		</section><section id="recent-posts-3" class="graceful-widget widget_recent_entries"><h2>Recent posts</h2>            <ul>
461                            <li class="graceful-recent-image-box">
462                    <div class="graceful-small-image-box" style="background-image: url( '' );">
463                    </div>
464                                    		<a href="https://www.kevinhouston.net/blog/2021/01/lessons-learned-from-covid-19-teaching/">Lessons Learned From Covid-19 Teaching</a>
465                </li>
466                            <li class="graceful-recent-image-box">
467                    <div class="graceful-small-image-box" style="background-image: url( '' );">
468                    </div>
469                                    		<a href="https://www.kevinhouston.net/blog/2020/03/mathematics-take-away-open-book-assessment/">Mathematics Take Away Open Book Assessment</a>
470                </li>
471                            <li class="graceful-recent-image-box">
472                    <div class="graceful-small-image-box" style="background-image: url( '' );">
473                    </div>
474                                    		<a href="https://www.kevinhouston.net/blog/2019/04/e-assessment/">E-assessment</a>
475                </li>
476                            <li class="graceful-recent-image-box">
477                    <div class="graceful-small-image-box" style="background-image: url( '' );">
478                    </div>
479                                    		<a href="https://www.kevinhouston.net/blog/2019/04/proof-from-the-particular-to-the-general/">Proof: From the particular to the general</a>
480                </li>
481                            <li class="graceful-recent-image-box">
482                    <div class="graceful-small-image-box" style="background-image: url( '' );">
483                    </div>
484                                    		<a href="https://www.kevinhouston.net/blog/2019/04/marks-for-writing/">Marks for writing</a>
485                </li>
486                        </ul>
487            </section><section id="archives-3" class="graceful-widget widget_archive"><h2 class="widget-title">Archive</h2>
488			<ul>
489					<li><a href='https://www.kevinhouston.net/blog/2021/01/'>January 2021</a></li>
490	<li><a href='https://www.kevinhouston.net/blog/2020/03/'>March 2020</a></li>
491	<li><a href='https://www.kevinhouston.net/blog/2019/04/'>April 2019</a></li>
492	<li><a href='https://www.kevinhouston.net/blog/2019/03/'>March 2019</a></li>
493	<li><a href='https://www.kevinhouston.net/blog/2018/05/'>May 2018</a></li>
494	<li><a href='https://www.kevinhouston.net/blog/2018/03/'>March 2018</a></li>
495	<li><a href='https://www.kevinhouston.net/blog/2017/10/'>October 2017</a></li>
496	<li><a href='https://www.kevinhouston.net/blog/2017/07/'>July 2017</a></li>
497	<li><a href='https://www.kevinhouston.net/blog/2016/05/'>May 2016</a></li>
498	<li><a href='https://www.kevinhouston.net/blog/2015/05/'>May 2015</a></li>
499	<li><a href='https://www.kevinhouston.net/blog/2015/04/'>April 2015</a></li>
500	<li><a href='https://www.kevinhouston.net/blog/2015/01/'>January 2015</a></li>
501	<li><a href='https://www.kevinhouston.net/blog/2014/12/'>December 2014</a></li>
502	<li><a href='https://www.kevinhouston.net/blog/2014/09/'>September 2014</a></li>
503	<li><a href='https://www.kevinhouston.net/blog/2014/07/'>July 2014</a></li>
504	<li><a href='https://www.kevinhouston.net/blog/2014/03/'>March 2014</a></li>
505	<li><a href='https://www.kevinhouston.net/blog/2014/02/'>February 2014</a></li>
506	<li><a href='https://www.kevinhouston.net/blog/2014/01/'>January 2014</a></li>
507	<li><a href='https://www.kevinhouston.net/blog/2013/12/'>December 2013</a></li>
508	<li><a href='https://www.kevinhouston.net/blog/2013/11/'>November 2013</a></li>
509	<li><a href='https://www.kevinhouston.net/blog/2013/10/'>October 2013</a></li>
510	<li><a href='https://www.kevinhouston.net/blog/2013/09/'>September 2013</a></li>
511	<li><a href='https://www.kevinhouston.net/blog/2013/08/'>August 2013</a></li>
512	<li><a href='https://www.kevinhouston.net/blog/2013/07/'>July 2013</a></li>
513	<li><a href='https://www.kevinhouston.net/blog/2013/06/'>June 2013</a></li>
514	<li><a href='https://www.kevinhouston.net/blog/2013/05/'>May 2013</a></li>
515	<li><a href='https://www.kevinhouston.net/blog/2013/04/'>April 2013</a></li>
516	<li><a href='https://www.kevinhouston.net/blog/2013/03/'>March 2013</a></li>
517	<li><a href='https://www.kevinhouston.net/blog/2013/02/'>February 2013</a></li>
518	<li><a href='https://www.kevinhouston.net/blog/2013/01/'>January 2013</a></li>
519	<li><a href='https://www.kevinhouston.net/blog/2012/12/'>December 2012</a></li>
520	<li><a href='https://www.kevinhouston.net/blog/2012/11/'>November 2012</a></li>
521	<li><a href='https://www.kevinhouston.net/blog/2012/10/'>October 2012</a></li>
522	<li><a href='https://www.kevinhouston.net/blog/2012/09/'>September 2012</a></li>
523	<li><a href='https://www.kevinhouston.net/blog/2012/08/'>August 2012</a></li>
524	<li><a href='https://www.kevinhouston.net/blog/2012/07/'>July 2012</a></li>
525	<li><a href='https://www.kevinhouston.net/blog/2012/06/'>June 2012</a></li>
526	<li><a href='https://www.kevinhouston.net/blog/2012/05/'>May 2012</a></li>
527	<li><a href='https://www.kevinhouston.net/blog/2012/04/'>April 2012</a></li>
528	<li><a href='https://www.kevinhouston.net/blog/2012/03/'>March 2012</a></li>
529	<li><a href='https://www.kevinhouston.net/blog/2012/02/'>February 2012</a></li>
530	<li><a href='https://www.kevinhouston.net/blog/2012/01/'>January 2012</a></li>
531	<li><a href='https://www.kevinhouston.net/blog/2011/12/'>December 2011</a></li>
532	<li><a href='https://www.kevinhouston.net/blog/2011/11/'>November 2011</a></li>
533	<li><a href='https://www.kevinhouston.net/blog/2011/10/'>October 2011</a></li>
534	<li><a href='https://www.kevinhouston.net/blog/2011/09/'>September 2011</a></li>
535	<li><a href='https://www.kevinhouston.net/blog/2011/08/'>August 2011</a></li>
536	<li><a href='https://www.kevinhouston.net/blog/2011/07/'>July 2011</a></li>
537	<li><a href='https://www.kevinhouston.net/blog/2011/06/'>June 2011</a></li>
538	<li><a href='https://www.kevinhouston.net/blog/2011/05/'>May 2011</a></li>
539	<li><a href='https://www.kevinhouston.net/blog/2011/04/'>April 2011</a></li>
540	<li><a href='https://www.kevinhouston.net/blog/2011/03/'>March 2011</a></li>
541	<li><a href='https://www.kevinhouston.net/blog/2011/02/'>February 2011</a></li>
542	<li><a href='https://www.kevinhouston.net/blog/2011/01/'>January 2011</a></li>
543	<li><a href='https://www.kevinhouston.net/blog/2010/12/'>December 2010</a></li>
544	<li><a href='https://www.kevinhouston.net/blog/2010/11/'>November 2010</a></li>
545	<li><a href='https://www.kevinhouston.net/blog/2010/10/'>October 2010</a></li>
546	<li><a href='https://www.kevinhouston.net/blog/2010/09/'>September 2010</a></li>
547			</ul>
548
549			</section><section id="text-4" class="graceful-widget widget_text"><h2 class="widget-title">Site hosted by:</h2>			<div class="textwidget">
549<script type="text/javascript" src="http://www.pixelinternet.co.uk/affiliate/scripts/banner.php?a_aid=kevihous&a_bid=ae84b573"></script>
549</div>
550		</section>	    	</aside>
551</div>
552
553		</div><!-- .main-content End -->
554		</main><!-- #primary End -->
555
556		<!-- Site Footer -->
557		<footer id="site-footer" class=" clear-fix">
558			<div class="site-footer-wrap wrapped-content">
559				
560
561    <div class="footer-bottom-wrap">
562        <!-- Scroll To Top -->
563        <span class="scrolltop">
564            <i class="fa fa fa-angle-up"></i>
565        </span>
566        
567        <div class="footer-copyright">
568                    </div>
569        
570        <div class="footer-credits">
571            Graceful Theme by             <a href="http://optimathemes.com/">
572                Optima Themes            </a>
573        </div>
574    </div>			</div><!-- .wrapped-content -->
575		</footer><!-- #site-footer -->
576
577				
578	</div><!-- #site-container -->
579
580<script type="text/javascript" src="http://www.kevinhouston.net/blog/wp-content/themes/graceful-minimal/assets/js/main.js?ver=1.0.4" id="graceful-main-js"></script>
580
581<!--stats_footer_test-->
581<script src="http://stats.wordpress.com/e-202640.js" type="text/javascript"></script>
vendor: 1 bytes, line 581
581
582<script type="text/javascript">
583st_go({blog:'16325488',v:'ext',post:'0'});
584var load_cmc = function(){linktracker_init(16325488,0,2);};
585if ( typeof addLoadEvent != 'undefined' ) addLoadEvent(load_cmc);
586else load_cmc();
587</script>
587
588
589</body>
590</html>
591
592<!-- Page cached by LiteSpeed Cache 5.7 on 2026-09-29 18:30:07 -->

Line numbers count LF bytes from the start of the resource, as the search results do. Vendor segments are library code the classifier recognised; they are stored but not indexed. Bytes are shown as Latin1 characters, one per byte.