CINXE.COM

<!DOCTYPE html><html lang="en-US"><head><title>Just a moment...</title><meta http-equiv="Content-Type" content="text/html; charset=UTF-8"><meta http-equiv="X-UA-Compatible" content="IE=Edge"><meta name="robots" content="noindex,nofollow"><meta name="viewport" content="width=device-width,initial-scale=1"><style>*{box-sizing:border-box;margin:0;padding:0}html{line-height:1.15;-webkit-text-size-adjust:100%;color:#313131;font-family:system-ui,-apple-system,BlinkMacSystemFont,Segoe UI,Roboto,Helvetica Neue,Arial,Noto Sans,sans-serif,Apple Color Emoji,Segoe UI Emoji,Segoe UI Symbol,Noto Color Emoji}body{display:flex;flex-direction:column;height:100vh;min-height:100vh}.main-content{margin:8rem auto;max-width:60rem;padding-left:1.5rem}@media (width <= 720px){.main-content{margin-top:4rem}}.h2{font-size:1.5rem;font-weight:500;line-height:2.25rem}@media (width <= 720px){.h2{font-size:1.25rem;line-height:1.5rem}}#challenge-error-text{background-image:url(data:image/svg+xml;base64,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);background-repeat:no-repeat;background-size:contain;padding-left:34px}@media (prefers-color-scheme:dark){body{background-color:#222;color:#d9d9d9}}</style><meta http-equiv="refresh" content="390"></head><body class="no-js"><div class="main-wrapper" role="main"><div class="main-content"><noscript><div class="h2"><span id="challenge-error-text">Enable JavaScript and cookies to continue</span></div></noscript></div></div><script>(function(){window._cf_chl_opt={cvId: '3',cZone: "www.columbia.edu",cType: 'managed',cRay: '913540ec69b1fdaa',cH: 'r46Oa0kFNwYYKOuyMchTaOwy6Tzfh7Pe_ivr3Y3C3Zc-1739789815-1.2.1.1-E.hBnE1R73b2EbaAGpWYLkLSe4L9pVXGHPMxe7CBcGpWx2zN.4Eq7bzrytz9g3wg',cUPMDTk: "\/~cs2035\/?__cf_chl_tk=yVhK0FZAUDkvbT48Cmyt2SAe3KBLmHD9CDvfSTYIm5Y-1739789815-1.0.1.1-Cyv4aaJsqxbYi21lRfsGG5F0XkzN8i1qXUMxNQtzTkg",cFPWv: 'b',cITimeS: '1739789815',cTTimeMs: '1000',cMTimeMs: '390000',cTplC: 0,cTplV: 5,cTplB: 'cf',cK: "",fa: "\/~cs2035\/?__cf_chl_f_tk=yVhK0FZAUDkvbT48Cmyt2SAe3KBLmHD9CDvfSTYIm5Y-1739789815-1.0.1.1-Cyv4aaJsqxbYi21lRfsGG5F0XkzN8i1qXUMxNQtzTkg",md: "f_Q1takIOuXkur0AYO5s28wXD5FmGEChPup5VTDABMA-1739789815-1.2.1.1-z.MvZv1uD.O2D.P.wVudlkf_i2vkBqUZzYE6an95S0jJdMKoO_hcBL2BgaYJueXY6WNS2yXol2PHM_rw1ulY79jIdlcEanBiN_8w5ADn9EOCKsouDUO86.qe4y_voMqDXepyLATo.zLLDv8iyN1ZTk9n4lZF4vgfSYywaqNjO9.JK0_aCeum8o9fqPAxhu1L8eV_VwFPfvcHb8bm9.HhyT9rThFbcFnw0uwzh3f.vzQ8wyyxaLy8.07phCAPZNFXpvM2zoH4IMV46gJfYdNlLatUL_xlLXgA_FRUHubi1wTKS8bktD_agA3LJRwHYNA8IXiA0dVZTnPHxiSo7gMk.XdvD2BxKUI_8Pw8jdgz06ZwmU6.yxY5AoQEiugjmN5YCK4L0mfikPb9xazYo0A2AoABbHLqvQVRySvSgLc0ADdqCO01eOGxgqRtT_yIh0ZqIo7oi66qTWfPOAlETnrydW_TOoDmIIjETTYs6F7ZPjWZ04s3zlo0n4dgBgNVEverIIJ_KGDpekXbu9aFNML3RZxXpTENPUnI_jCh7TmdR01mwizAyYeChk.8_AeyyJ2MLWOEhf3mbLf5AhFgT78gj2Oo8QGYEss.QPfahgLyVQbw3Q5O9w.1Ith4FYnhaOZKYmv1fFRJR9nkmHPCi6ImwrfHGOpu8sXDUyob1vDjXFkL5LEI_sqxar_WYQec4kUvMEp1mNWWQFHf1svU81Mo29yHt1F3fiA_kvBaiPf0lBUG2wWkWNrs.Jwz5Vo1C60kew7XeMKkkEbBd5jnQrrnfsgXVKXwMSiC9VPg1vLO.b854iJEy_FMPT9.AkhHXwuQuiYoazfC5io0tVwD9BHjDkAaUxfO0ua.EH9lo.fA4Zflie8o1N1NRJfRBEM_VgNegbCnqNirmX0jpjjweunVzgKnIGLWSjCOykmQdfQu3nR0D12Q6bWvVbM33EUjrpGfyx9ux0AkDqowC.c0Umi0yxlbpZHmUQ.9GzHcuVSofnM1HrExIgYOCjDy5b9X7glMubOONNBNX7Cu.GmfMOBG_I4t4KQNp8rAPA5P0y80pMS8hi37dcBso_.dy.epvRH.dyXNOFhniwx.4wgREPMq_RPY8Zs4rIUgJGGWwO3CfMp5EYHFtMIHi3mkKiRLDsNAzI4Hq0MObVvWf8Flqt96_B.xhSKZnxFIymeMILTD6n9blbINkRRyjzPUqnlTHOs4pYi8QcGc8Yeo9kzhbFPbZkJO8TGruyliaiPoUFv0M.laSsUS.vSZCGrprPHfAuBuSCN45DeB7pwwgsWDVGeFH6upn8KsfZ297axprBiW7Mq8zJlVQyjJWw6bZOM3yziRhV1cKAR8yF_jXRLiqsR7G0WQWWU_LQz8hYS8sEJk0JSYpVTQEYcHJRuRqMCa1D_1l.PG886ikAVF.1MaLuvQ2HunoOEt7RL5ktKJAzUF8R4vymqii8a.NVnpcQXFMIjZnB18zD6dYf54B1DaLneExEIQMYU7luxa2jMy5aOWdeaayI0H42RmVlMWnJjspmA9dkjVoKhLlbxm7GQvPtoofggJrTXndpBZpj_B793UT3H1EcvKKAYu5e7B6kstcfaEKJ3IWrH8bkSthSZo1BaHgd9HWICqZ5YTyHmb2feolW6RDS5k5wnqyLL4hXmBzMVivwm2pi2HtbsCF.LY6DuRuqxHjKj7IDbmV_7Eo9Vx3wu9cTmRsh15Syb88Gh4o7ocyoIVSnUkAtRAfAchLe5tT3pgx_dzBaIocVASHX0gnvjdA7qItZNPae_M9Jk4lH6B9DNq.m32sk8HKVQ0BqQscApPXWjEwoAjYg1NCQJFxPUiEXVZSnO6Zx44g_p1CYzR0VqVdCJjZBnpfq4jj9bx.kNdQTexneKrXkN.f76SRQRKNmQoKW7_Y2IuIZVVCWMgwYdrp.TiihbystUYf06Z3_6i1iWRcDKpvg88F1q2AqDWgrWbuSoh.HFLnrmbcMJxMb0Zxjn3THD.AobF60n8yTwpngroWzkckEmmpNxij0OyGiOa0c5yjqXn7onVdUsHW_XFxJIW7Sgo37qrvu4sdnCT4dIxtntS_TjUFXQAWl1349AADdvYnXB3RgNP8Pcwu7LF1uEA4U0WkBkQAO26gRQV8oEcDVB8fgkBZYVthysvFbW.nFCMXTjn9zRPUIiQr2X8ZhdWqcGOJifw1DyxGXiIOg.qKzRH2q8w3co_Vic3Dg_c5llgAAgBvysZ77onRclOe3ykY6FqhMhj4uwGh3H01CQqfjah5VVl3A9fc.Ve6mA2zsLHOGYb3VMXrpNSs5W0qSM1Ok4L4JO90BOiqvQ7iJep4xuxZVqOiLXhKew_vyOW8yJTZ86rsK9v4mTJPzLSjx8..rNm_57RXp_kPqyMrDFJn3YG6ls5yM3zN_IcF98M4jEPa.wDRZk.g7xOqkB3OqXDiGQS40hnWfFDKBjA5S1YlBVqdM52BYvkxnFWzPE6OOGGzZxBmaPlglp42G_.kNVG40bZSIpblwFpBQ",mdrd: "h1HnzK3p7YcNsm2HLjgYHZ2W4UJmuozybJXd_PbM3Sw-1739789815-1.2.1.1-0hQxt_B5M_2dvIS9yZ8_lYX9tIFnkdQI624uQHe9iR6Rdfcb71jADD2wJ2avc0bYXblL3R0K1LzYF7CsjQe3CLyiNWZjUMQSTvNYXqPTeRCDgPZWJtPQz.3FIRD7PL0su8DmVbHXQg6whfDLSM_Mu4nz72gPhzdPWp8CGxhPRcvW3p6txDc8iaLZkVnZkIhG66cByMPfCXOqGFKVeWO3woon0X_ZhRBie_2S616aHcca._bhT6gA0g4cnrKp92yQ_D.5E5tteSGoSuwvROMcOzJLBUTGlrwa7BU8Fnh7Dd7I4jAqAw0dqOAZ1Ysd8l6PbYLKBTJd3kKnTpoBLhf51r68ezjYl6wyJixQWzo52G2FmmZ1NupyXT8AIqZeoZyMbI0SS1mKmBSW_iTJuDdh_ealLgpARFDjyJkUK0HRRMRs1kQvuPIT6SWaOITBbtCsdCmIWzPwZ_4xnRwSBO7tIKoW.gy6t7F9BFL1AzO0hNx4NClvfS8ZfXh1ktmELHxxaznmYAECRTWPf6WRWdJP2AE9xYbe_Pw7iWmCISaaT.1R43lverKZ8cR60kqxt9OhLH03nU9CGot.zz1aqMThay1X9miZKQ33ln17waEtMKJUWPuSXDNF8lSJhCtsvmYybz9M.dodCuLLRZnMLzxOasYh.RLu5GNsePiSd7BsJQk6JPN7QX044WGnAie8pppfeDcfA08_bUnTZjU0Az7iQA"};var cpo = document.createElement('script');cpo.src = '/cdn-cgi/challenge-platform/h/b/orchestrate/chl_page/v1?ray=913540ec69b1fdaa';window._cf_chl_opt.cOgUHash = location.hash === '' && location.href.indexOf('#') !== -1 ? '#' : location.hash;window._cf_chl_opt.cOgUQuery = location.search === '' && location.href.slice(0, location.href.length - window._cf_chl_opt.cOgUHash.length).indexOf('?') !== -1 ? '?' : location.search;if (window.history && window.history.replaceState) {var ogU = location.pathname + window._cf_chl_opt.cOgUQuery + window._cf_chl_opt.cOgUHash;history.replaceState(null, null, "\/~cs2035\/?__cf_chl_rt_tk=yVhK0FZAUDkvbT48Cmyt2SAe3KBLmHD9CDvfSTYIm5Y-1739789815-1.0.1.1-Cyv4aaJsqxbYi21lRfsGG5F0XkzN8i1qXUMxNQtzTkg" + window._cf_chl_opt.cOgUHash);cpo.onload = function() {history.replaceState(null, null, ogU);}}document.getElementsByTagName('head')[0].appendChild(cpo);}());</script></body></html>