加州大學洛杉磯分校數(shù)學類科研
來源:哈魯教育 2018-07-03
加州大學洛杉磯分校數(shù)學類科研
UCLA MATH Research
科研時間:
6月1日--9月1日,每期時間長度為3—4周
(針對假期只有3周的學生,可選3周實地+1周遠程,確??蒲惺斋@)
科研主題:
UCLA數(shù)學類頂尖科研;(Hanoi tower, SET game, games with potential functions)
面向對象:
以計劃申請美國名校數(shù)學類(基礎數(shù)學、應用數(shù)學)、物理類、統(tǒng)計類、計算機類相關專業(yè)的本科生、研究生為主
科研概述:
This research is designed to be an eye opener for college level and high school level students. The point is to provide a peek at advanced mathematics, apply them in ways beyond your imagination, and provide you with both an opportunity to learn and an opportunity to do research, if you are interested and capable.
Through this research, you will be introduced to a series of common games and puzzles, hopefully already known to you. We shall study some of them in depth, and you shall solve some of them yourselves, and maybe even encounter a few open problems in mathematics. The math awaits you are mostly combinatorics and group theory, but a few ideas from topology, geometry and analysis will nonetheless find their way into the research.
科研內(nèi)容:
STEP1: Overview
1. What is it like to be a math graduate student in the US;
2. A few puzzle problems to think about for the rest of the REU;
3. Some cool set theory unknown to most people.
STEP2: 15 puzzle
1. Quick solution to 15 puzzle;
2. Symmetric groups and alternating groups;
3. Fundamental groups;
4. Generalized 15 puzzle.
STEP3: Rubik’s cube
1. Homomorphisms of groups.
2. Symmetries on Rubik’s cube;
3. Orientations on Rubik’s cube;
4. Con?gurations of Rubik’s cube.
Other topics if time permits: Hanoi tower, SET game, games with potential functions, etc.
科研亮點:
1. 進入美國名校實驗室/科研組,接觸尖端科學
為未來赴美深造做準備;科研經(jīng)歷是美國名校申請的基石,頂級名校的科研項目是對學生有能力完成名校學業(yè)最好的證明。
2. 師從導師開展實驗項目
高層次的人脈和校友關系,與學生為伍的人是諾貝爾獎獲得者、美國科學院院士、教授、名校博士、碩士,學生將體驗到世界最頂級學術專家們的思想和氣質(zhì)。
3. 獲得導師推薦信和科研證書
對于優(yōu)秀學生可以獲得名校導師的推薦信,大大助力未來的留學申請。
4. 全天候專業(yè)英語環(huán)境,迅速提升專業(yè)水平
提升溝通和專業(yè)英語水平,提升專業(yè)知識和能力,用實踐使學生的理論知識更加具體形象。
5. 高含金量收獲助力未來留學深造及就業(yè)
在名校導師指導下的科研過程將幫助學生明確自身發(fā)展方向,不斷深化對于美國學界的了解與認同,幫助參與學生及家長明確未來的學校及專業(yè)申請方向;從而更好的明確留學的目的與意義,擺脫盲目,獲得真知。
科研收獲:
1.科研完成時,學生將會全面了解數(shù)學領域基本知識和最新進展。
2.挑戰(zhàn)自身潛能,切身體會UCLA頂尖科研環(huán)境,在嚴苛的訓練下快速成長。
3.極大拓寬視野,實地感受國內(nèi)外科研區(qū)別。通過此次科研,參與學生將會對留學名校有個清晰的認識,并依此做出最優(yōu)的人生規(guī)劃。
4.學生將有機會與頂尖教授零距離交流套磁,了解UCLA的內(nèi)部申請信息。
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