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{{short description|American mathematician}}
{{for|the American jazz musician|Arnold Ross (musician)}}
{{for|the American jazz musician|Arnold Ross (musician)}}
{{Infobox scientist
{{Infobox scientist
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| caption = Ross in 1970
| caption = Ross in 1970
| birth_date = {{Birth date|1906|08|24}}
| birth_date = {{Birth date|1906|08|24}}
| birth_place = [[Chicago]], [[Illinois]], USA
| birth_place = [[Chicago]], [[Illinois]], US
| death_date = {{Death date and age|2002|09|25|1906|08|24}}
| death_date = {{Death date and age|2002|09|25|1906|08|24}}
| death_place =
| death_place =
| resting_place =
| resting_place_coordinates = <!-- {{Coord|LAT|LONG|type:landmark|display=inline,title}} -->
| residence =
| citizenship = United States
| fields = [[Number theory]]
| fields = [[Number theory]]
| workplaces = [[California Institute of Technology]], [[St. Louis University]], [[University of Notre Dame]], [[Ohio State University]]
| workplaces = [[California Institute of Technology]], [[St. Louis University]], [[University of Notre Dame]], [[Ohio State University]]
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| doctoral_advisor = [[L. E. Dickson]]
| doctoral_advisor = [[L. E. Dickson]]
| academic_advisors = [[Samuil Shatunovsky]], <br>[[E. H. Moore]]
| academic_advisors = [[Samuil Shatunovsky]], <br>[[E. H. Moore]]
| doctoral_students =
| doctoral_students = [[Margaret Willerding]]
| notable_students =
| notable_students =
| known_for = [[Mathematics education]] <br>(Ross Mathematics Program)
| known_for = [[Mathematics education]] <br>(Ross Mathematics Program)
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}}
}}


'''Arnold Ephraim Ross''' (August 24, 1906 – September 25, 2002) was a [[mathematician]] and [[Mathematics education|educator]] who founded the Ross Mathematics Program, a [[number theory]] summer program for [[Gifted education|gifted]] [[High school (United States)|high school]] students. He was born in Chicago, but spent his youth in [[Odessa, Ukraine]], where he studied with [[Samuil Shatunovsky]]. Ross returned to Chicago and enrolled in [[University of Chicago]] graduate coursework under [[E. H. Moore]], despite his lack of formal academic training. He received his Ph.D. and married his wife, Bee, in 1931.
'''Arnold Ephraim Ross''' (August 24, 1906 – September 25, 2002) was a [[mathematician]] and [[Mathematics education|educator]] who founded the Ross Mathematics Program, a [[number theory]] summer program for [[Gifted education|gifted]] [[High school (United States)|high school]] students. He was born in Chicago, but spent his youth in [[Odesa, Ukraine]], where he studied with [[Samuil Shatunovsky]]. Ross returned to Chicago and enrolled in [[University of Chicago]] graduate coursework under [[E. H. Moore]], despite his lack of formal academic training. He received his Ph.D. and married his wife, Bee, in 1931.


Ross taught at several institutions including [[St. Louis University]] before becoming chair of [[University of Notre Dame]]'s mathematics department in 1946. He started a teacher training program in mathematics that evolved into the Ross Mathematics Program in 1957 with the addition of high school students. The program moved with him to [[Ohio State University]] when he became their department chair in 1963. Though forced to retire in 1976, Ross ran the summer program until 2000. He had worked with over 2,000 students during more than forty summers.
Ross taught at several institutions including [[St. Louis University]] before becoming chair of [[University of Notre Dame]]'s mathematics department in 1946. He started a teacher training program in mathematics that evolved into the [[Ross Mathematics Program]] in 1957 with the addition of high school students. The program moved with him to [[Ohio State University]] when he became their department chair in 1963. Though forced to retire in 1976, Ross ran the summer program until 2000. He had worked with over 2,000 students during more than forty summers.


The program is known as Ross's most significant work. Its attendees have since continued on to prominent research positions across the sciences. His program inspired several offshoots and was recognized by mathematicians as highly influential. Ross has received an [[honorary doctorate]] and several professional association awards for his instruction and service.
The program is known as Ross's most significant work. Its attendees have since continued on to prominent research positions across the sciences. His program inspired several offshoots and was recognized by mathematicians as highly influential. Ross has received an [[honorary doctorate]] and several professional association awards for his instruction and service.
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== Early life and career ==
== Early life and career ==


[[File:Arnold Ross as young boy in school uniform.jpg|thumb|left|Ross as young boy in school uniform]] Ross was born Arnold Ephraim Chaimovich<ref name="NAMS 2001"/> on August 24, 1906, in [[Chicago]] to Ukrainian-Jewish immigrants.<ref name="NAMS 1996"/> He was an only child.<ref name="NAMS 2001"/> His mother supported the family as a physical therapist.<ref name="NAMS 2001"/> Ross returned to [[Odessa]], [[Ukraine]] with his mother in 1909 for assistance from her extended family,<ref name="NAMS 2001"/> and stayed once [[World War I]] and the [[Russian Revolution]] broke out.<ref name="NAMS 1996"/> The two events led to widespread famine and economic woe in the region.<ref name="NAMS 2001"/> Ross learned Russian at the behest of his mother, and developed a love of the theater and language.<ref name="NAMS 2001"/> Ross's mother encouraged him to read, which he did often, and subscribed to a private library since Odessa had no public library.<ref name="NAMS 2001"/> He credited his favorite uncle, an X-ray diagnostician, with introducing him to mathematics.<ref name="NAMS 2001"/> The uncle had hired [[Samuil Shatunovsky]] to tutor his talented son, and Ross asked to join in.<ref name="NAMS 2001"/> As money meant little due to inflation, Shatunovsky was paid to tutor the two boys with a pound of French hard candy.<ref name="NAMS 2001"/> During this time, Ross was not taught with textbooks or lectured on geometric proofs.<ref name="NAMS 2001"/> His geometry teacher would ask the class to prove and justify ideas on the blackboard per trial and error.<ref name="NAMS 2001"/> Many universities were closed due to the famine, but [[Odessa University]] reopened and let a small group of adolescents attend, including Ross.<ref name="NAMS 2001"/>
[[File:Arnold Ross as young boy in school uniform.jpg|thumb|left|Ross as young boy in school uniform]] Ross was born Arnold Ephraim Chaimovich<ref name="NAMS 2001"/> on August 24, 1906, in [[Chicago]] to Ukrainian-Jewish immigrants.<ref name="NAMS 1996"/> He was an only child.<ref name="NAMS 2001"/> His mother supported the family as a physical therapist.<ref name="NAMS 2001"/> Ross returned to [[Odesa]], [[Ukraine]] with his mother in 1909 for assistance from her extended family,<ref name="NAMS 2001"/> and stayed once [[World War I]] and the [[Russian Revolution]] broke out.<ref name="NAMS 1996"/> The two events led to widespread famine and economic woe in the region.<ref name="NAMS 2001"/> Ross learned Russian at the behest of his mother, and developed a love of the theater and language.<ref name="NAMS 2001"/> Ross's mother encouraged him to read, which he did often, and subscribed to a private library since Odesa had no public library.<ref name="NAMS 2001"/> He credited his favorite uncle, an X-ray diagnostician, with introducing him to mathematics.<ref name="NAMS 2001"/> The uncle had hired [[Samuil Shatunovsky]] to tutor his talented son, and Ross asked to join in.<ref name="NAMS 2001"/> As money meant little due to inflation, Shatunovsky was paid to tutor the two boys with a pound of French hard candy.<ref name="NAMS 2001"/> During this time, Ross was not taught with textbooks or lectured on geometric proofs.<ref name="NAMS 2001"/> His geometry teacher would ask the class to prove and justify ideas on the blackboard per trial and error.<ref name="NAMS 2001"/> Many universities were closed due to the famine, but [[Odesa University]] reopened and let a small group of adolescents attend, including Ross.<ref name="NAMS 2001"/>


[[File:Arnold Chaimovich as a young man in Odessa, around 1922 (?).jpg|thumb|right|Ross in Odessa circa 1922]] Ross left Odessa—now part of the USSR—in 1922 with the intention of returning to Chicago and studying [[topology]] with [[E. H. Moore]] at the [[University of Chicago]].<ref name="NAMS 2001"/> After negotiating his way home, he worked at a family friend's bookbinding shop and continued to learn English at the [[Lewis Institute]].<ref name="NAMS 2001"/> He also changed his surname from Chaimovich to Ross in 1922.<ref name="NAMS 2003"/> Ross used his salary from a year at the shop to enroll for one term at the University of Chicago in Moore's course.<ref name="NAMS 2001"/> Moore gave Ross special attention, knowing his untraditional background, and arranged for Ross to attend the topology class as the sole undergraduate.<ref name="NAMS 2001"/>
[[File:Arnold Chaimovich as a young man in Odessa, around 1922 (?).jpg|thumb|right|Ross in Odesa circa 1922]] Ross left Odesa—now part of Ukraine—in 1922 with the intention of returning to Chicago and studying [[topology]] with [[E. H. Moore]] at the [[University of Chicago]].<ref name="NAMS 2001"/> After negotiating his way home, he worked at a family friend's bookbinding shop and continued to learn English at the [[Lewis Institute]].<ref name="NAMS 2001"/> He also changed his surname from Chaimovich to Ross in 1922.<ref name="NAMS 2003"/> Ross used his salary from a year at the shop to enroll for one term at the University of Chicago in Moore's course.<ref name="NAMS 2001"/> Moore gave Ross special attention, knowing his untraditional background, and arranged for Ross to attend the topology class as the sole undergraduate.<ref name="NAMS 2001"/>


In Moore's teaching style, he would propose a conjecture and task the students with proving it.<ref name="NAMS 2001"/> Students could respond with counter-conjectures that they would defend.<ref name="NAMS 2001"/> Ross found Moore's method exciting,<ref name="NAMS 2001"/> and his pedagogy influenced Ross's own.<ref name="NAMS 1996"/> Ross graduated with a B.S. degree<ref name="AMM 1986"/> and continued his study as [[Leonard Eugene Dickson]]'s research assistant.<ref name="NAMS 1996"/> Ross earned a M.S. degree<ref name="AMM 1986"/> and finished his Ph.D. in number theory at the University of Chicago in 1931 with Dickson as his adviser.<ref name="NAMS 1996"/> Ross's dissertation was entitled "On Representation of Integers by Indefinite Ternary Quadratic Forms".<ref name="NAMS 2001"/> He did not pay tuition after his first quarter, which he credits to Dickson.<ref name="NAMS 2001"/>
In Moore's teaching style, he would propose a conjecture and task the students with proving it.<ref name="NAMS 2001"/> Students could respond with counter-conjectures that they would defend.<ref name="NAMS 2001"/> Ross found Moore's method exciting,<ref name="NAMS 2001"/> and his pedagogy influenced Ross's own.<ref name="NAMS 1996"/> Ross graduated with a B.S. degree<ref name="AMM 1986"/> and continued his study as [[Leonard Eugene Dickson]]'s research assistant.<ref name="NAMS 1996"/> Ross earned a M.S. degree<ref name="AMM 1986"/> and finished his Ph.D. in number theory at the University of Chicago in 1931 with Dickson as his adviser.<ref name="NAMS 1996"/> Ross's dissertation was entitled "On Representation of Integers by Indefinite Ternary Quadratic Forms".<ref name="NAMS 2001"/> He did not pay tuition after his first quarter, which he credits to Dickson.<ref name="NAMS 2001"/>
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== Ross Mathematics Program ==
== Ross Mathematics Program ==


While at Notre Dame in 1947, Ross began a mathematics program that prioritized what he described as "the act of personal discovery through observation and experimentation" for high school and junior college teachers.<ref name="NAMS 2001"/> In 1957, the program expanded via the [[National Science Foundation]]'s post-[[Sputnik]] funds for teacher retraining, and Ross let high school students attend.<ref name="NAMS 2001"/> This expansion became the Ross Mathematics Program,<ref name="NAMS 2001"/> a summer mathematics program for gifted high school students.<ref name="NAMS 1996"/> The program lasts eight weeks and brings students with no prior knowledge to topics such as [[Gaussian integers]] and [[quadratic reciprocity]].<ref name="NAMS 1996"/> Though the program teaches number theory, by its Gauss-inspired<ref name="Bauldry 2011"/> motto, "Think deeply of simple things", its primary goal is to offer precollege students an intellectual experience<ref name="NAMS 1996"/> as what he described as "a vivid apprenticeship to a life of exploration".<ref name="NAMS 2001"/><ref name="NAMS 1998"/> The program is known for its intensity, and is considered America's "most rigorous number theory program", according to ''What High Schools Don't Tell You''.<ref name="Wissner-Gross 2007"/> Ross was known to say, "No one leaves the program unchanged."<ref name="MAA FOCUS 2003"/>
While at Notre Dame in 1947, Ross began a mathematics program that prioritized what he described as "the act of personal discovery through observation and experimentation" for high school and junior college teachers.<ref name="NAMS 2001"/> In 1957, the program expanded via the [[National Science Foundation]]'s post-[[Sputnik]] funds for teacher retraining, and Ross let high school students attend.<ref name="NAMS 2001"/> This expansion became the Ross Mathematics Program,<ref name="NAMS 2001"/> a summer mathematics program for talented high school students.<ref name="NAMS 1996"/> The program lasts eight weeks and brings students with no prior knowledge to topics such as [[Gaussian integers]] and [[quadratic reciprocity]].<ref name="NAMS 1996"/> Though the program teaches number theory, by its Gauss-inspired<ref name="Bauldry 2011"/> motto, "Think deeply of simple things," its primary goal is to offer precollege students an intellectual experience<ref name="NAMS 1996"/> as what he described as "a vivid apprenticeship to a life of exploration."<ref name="NAMS 2001"/><ref name="NAMS 1998"/> The program is known for its intensity, and is considered America's "most rigorous number theory program."<ref name="Wissner-Gross 2007"/> Ross was known to say, "No one leaves the program unchanged."<ref name="MAA FOCUS 2003"/>


{{Quote box |quote=This emphasis on computation alone too often produces students who have never practiced thinking for themselves, who have never asked why things work the way they do, who are not prepared to lead the way to future scientific innovation. It is precisely this independence of thought and questioning attitude that the Ross Program strives to nurture. |source=Ross Program brochure<ref name="Wissner-Gross 2007"/> |quoted=1 |align=right |width=300px }}
{{Quote box |quote=This emphasis on computation alone too often produces students who have never practiced thinking for themselves, who have never asked why things work the way they do, who are not prepared to lead the way to future scientific innovation. It is precisely this independence of thought and questioning attitude that the Ross Program strives to nurture. |source=Ross Program brochure<ref name="Wissner-Gross 2007"/> |quoted=1 |align=right |width=300px }}


The program usually has 40–50 first-year students, 15 advanced students, and 15 counselors.<ref name="NAMS 1996"/> Students are admitted by application—which includes a set of mathematical questions—or by showing "a great eagerness to learn".<ref name="NAMS 1996"/> First-year students meet daily for lectures in elementary number theory and thrice weekly for problem seminars.<ref name="NAMS 1996"/> They are encouraged to think like scientists and devise their own proofs and conjectures to the problems posed,<ref name="NAMS 1996"/> which occupies most of their free time.<ref name="Wissner-Gross 2007"/> Ross designed the daily [[problem set]]s,<ref name="MAA FOCUS 2003"/> and many questions contain his signature directions: "Prove or disprove and salvage if possible."<ref name="NAMS 2001"/> Successful students are asked to return as students and counselors in future summers.<ref name="NAMS 1996"/> Returning students revisit the daily lectures and help first-years with their questions.<ref name="NAMS 1996"/> They also can take advanced courses such as [[combinatorics]]<ref name="NAMS 1996"/> and graduate seminars.<ref name="MAA FOCUS 2003"/> Student problem sets are graded daily by the live-in counselors.<ref name="NAMS 1996"/>
The program usually has 40–50 first-year students, 15 junior counselors, and 15 counselors.<ref name="NAMS 1996"/> Students are admitted by application—which includes a set of mathematical questions—or by showing "a great eagerness to learn."<ref name="NAMS 1996"/> First-year students meet daily for lectures in elementary number theory and thrice weekly for problem seminars.<ref name="NAMS 1996"/> They are encouraged to think like scientists and devise their own proofs and conjectures to the problems posed,<ref name="NAMS 1996"/> which occupies most of their free time.<ref name="Wissner-Gross 2007"/> Ross designed the daily [[problem set]]s,<ref name="MAA FOCUS 2003"/> and many questions contain his signature directions: "Prove or disprove and salvage if possible."<ref name="NAMS 2001"/> Successful students are asked to return as junior counselors and counselors in future summers.<ref name="NAMS 1996"/> Junior counselors revisit the daily lectures and help first-years with their questions.<ref name="NAMS 1996"/> They also can take advanced courses such as [[combinatorics]]<ref name="NAMS 1996"/> and graduate seminars.<ref name="MAA FOCUS 2003"/> Student problem sets are graded daily by the live-in counselors.<ref name="NAMS 1996"/>


The program was funded in the 1960s by a [[National Science Foundation]] (NSF) program that supported summer programs in science education, but not returning students.<ref name="NAMS 1996"/> As NSF support fluctuates, the program has been funded by various means including gifts from donors, scholarships from businesses, a [[National Security Agency]] grant, the university, and its mathematics department.<ref name="NAMS 1996"/> It also receives financial support from the [[Clay Mathematics Institute]].<ref name="NAMS 2001"/><ref name="Wissner-Gross 2007"/>
The program was funded in the 1960s by a [[National Science Foundation]] (NSF) program that supported summer programs in science education, but not returning students.<ref name="NAMS 1996"/> As NSF support fluctuates, the program has been funded by various means including gifts from donors, scholarships from businesses, a [[National Security Agency]] grant, the university, and its mathematics department.<ref name="NAMS 1996"/> It also receives financial support from the [[Clay Mathematics Institute]].<ref name="NAMS 2001"/><ref name="Wissner-Gross 2007"/>


The program grew rapidly with input from prominent mathematicians such as [[Ram Prakash Bambah]], [[Hans Zassenhaus]], [[Thoralf Skolem]], and [[Max Dehn]].<ref name="NAMS 1996"/> In the 1960s and 1970s, Ross brought mathematicians including Zassenhaus, [[Kurt Mahler]], and [[Dijen K. Ray-Chaudhuri]] to teach there regularly.<ref name="NAMS 2001"/> Ross left Notre Dame to become chair of [[Ohio State University]]'s mathematics department in 1963, and the program followed in the 1964 summer.<ref name="NAMS 1996"/> The program briefly moved to the University of Chicago in the summers of 1975–1978 at mathematician [[Felix Browder]]'s invitation.<ref name="NAMS 1996"/> The program is unadvertised and depends on personal contacts and word of mouth to propagate.<ref name="NAMS 2001"/><ref name="NAMS 1996"/><ref name="Wissner-Gross 2007"/> It is recognized by mathematicians as one of the best mathematics programs for high school students.<ref name="Wissner-Gross 2007"/>
The program grew rapidly with input from prominent mathematicians such as [[Ram Prakash Bambah]], [[Hans Zassenhaus]], [[Thoralf Skolem]], and [[Max Dehn]].<ref name="NAMS 1996"/> In the 1960s and 1970s, Ross brought mathematicians including Zassenhaus, [[Kurt Mahler]], and [[Dijen K. Ray-Chaudhuri]] to teach there regularly.<ref name="NAMS 2001"/> Ross left Notre Dame to become chair of [[Ohio State University]]'s mathematics department in 1963, and the program followed in the 1964 summer.<ref name="NAMS 1996"/> The program briefly moved to the University of Chicago in the summers of 1975–1978 at mathematician [[Felix Browder]]'s invitation.<ref name="NAMS 1996"/> The program is unadvertised and depends on personal contacts and word of mouth to propagate.<ref name="NAMS 2001"/><ref name="NAMS 1996"/><ref name="Wissner-Gross 2007"/> It is recognized by mathematicians as one of the best mathematics programs for high school students.<ref name="Wissner-Gross 2007"/>

Admission to the program is competitive, with an approximately 15% acceptance rate. <ref>{{cite web |title=Frequently Asked Questions |url=https://rossprogram.org/students/faq/ |website=The Ross Mathematics Program |access-date=22 October 2023}}</ref>


== Retirement and death ==
== Retirement and death ==
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{{reflist|2|refs=
{{reflist|2|refs=


<ref name="AMM 1986">{{cite journal|last1=Lax |first1=Anneli |authorlink=Anneli Cahn Lax |last2=Woods |first2=Alan C. |title=Award for Distinguished Service to Professor Arnold Ephraim Ross |date=April 1986 |journal=[[American Mathematical Monthly]] |publisher=[[Mathematical Association of America]] |issn=0002-9890 |volume=93 |issue=4 |pages=245–246 |jstor=2323671 |doi=10.1080/00029890.1986.11971798 }}</ref>
<ref name="AMM 1986">{{cite journal|last1=Lax |first1=Anneli |author-link=Anneli Cahn Lax |last2=Woods |first2=Alan C. |title=Award for Distinguished Service to Professor Arnold Ephraim Ross |date=April 1986 |journal=[[American Mathematical Monthly]] |publisher=[[Mathematical Association of America]] |issn=0002-9890 |volume=93 |issue=4 |pages=245–246 |jstor=2323671 |doi=10.1080/00029890.1986.11971798 }}</ref>


<ref name="Bauldry 2011">{{cite book|author=William C. Bauldry|title=Introduction to Real Analysis: An Educational Approach|url=https://books.google.com/books?id=eClOhyJmxDkC&pg=PA46|accessdate=September 20, 2013|date=9 September 2011|publisher=John Wiley & Sons|isbn=978-1-118-16443-3|page=46}}</ref>
<ref name="Bauldry 2011">{{cite book|author=William C. Bauldry|title=Introduction to Real Analysis: An Educational Approach|url=https://books.google.com/books?id=eClOhyJmxDkC&pg=PA46|access-date=September 20, 2013|date=9 September 2011|publisher=John Wiley & Sons|isbn=978-1-118-16443-3|page=46}}</ref>


<ref name="Edgar 2007">{{cite book|last=Edgar|first=Gerald A.|title=Measure, Topology, and Fractal Geometry|url=https://books.google.com/books?id=dk2vruTv0_gC&pg=PR11|accessdate=September 20, 2013|date=October 23, 2007|publisher=Springer-Verlag|isbn=978-0-387-74749-1|page=XI}}</ref>
<ref name="Edgar 2007">{{cite book|last1=Edgar|first1=Gerald A.|title=Measure, Topology, and Fractal Geometry|url=https://books.google.com/books?id=dk2vruTv0_gC&pg=PR11|access-date=September 20, 2013|date=October 23, 2007|publisher=Springer-Verlag|isbn=978-0-387-74749-1|page=XI}}</ref>


<ref name="MAA FOCUS 2002">{{cite journal|url=http://www.maa.org/sites/default/files/pdf/pubs/dec02web.pdf |last=Stevens |first=Glenn |title=Memories of Arnold Ross |date=December 2002 |journal=[[MAA FOCUS]] |publisher=[[Mathematical Association of America]] |issn=0731-2040 |volume=22 |issue=9 |page=22 |accessdate=September 20, 2013 |archiveurl=https://web.archive.org/web/20130921060013/http://www.maa.org/sites/default/files/pdf/pubs/dec02web.pdf |archivedate=September 21, 2013 |deadurl=no |df= }}</ref>
<ref name="MAA FOCUS 2002">{{cite journal|url=http://www.maa.org/sites/default/files/pdf/pubs/dec02web.pdf |last1=Stevens |first1=Glenn |title=Memories of Arnold Ross |date=December 2002 |journal=[[MAA FOCUS]] |publisher=[[Mathematical Association of America]] |issn=0731-2040 |volume=22 |issue=9 |page=22 |access-date=September 20, 2013 |archive-url=https://web.archive.org/web/20130921060013/http://www.maa.org/sites/default/files/pdf/pubs/dec02web.pdf |archive-date=September 21, 2013 |url-status=live }}</ref>


<ref name="MAA FOCUS 2003">{{cite journal|url=http://www.maa.org/sites/default/files/pdf/pubs/jan03.pdf |last=Stevens |first=Glenn |title=Memories of Arnold Ross |date=January 2003 |journal=[[MAA FOCUS]] |publisher=[[Mathematical Association of America]] |issn=0731-2040 |volume=23 |issue=1 |page=17 |accessdate=September 20, 2013 |archiveurl=https://web.archive.org/web/20130921060601/http://www.maa.org/sites/default/files/pdf/pubs/jan03.pdf |archivedate=September 21, 2013 |deadurl=no |df= }}</ref>
<ref name="MAA FOCUS 2003">{{cite journal|url=http://www.maa.org/sites/default/files/pdf/pubs/jan03.pdf |last1=Stevens |first1=Glenn |title=Memories of Arnold Ross |date=January 2003 |journal=[[MAA FOCUS]] |publisher=[[Mathematical Association of America]] |issn=0731-2040 |volume=23 |issue=1 |page=17 |access-date=September 20, 2013 |archive-url=https://web.archive.org/web/20130921060601/http://www.maa.org/sites/default/files/pdf/pubs/jan03.pdf |archive-date=September 21, 2013 |url-status=live }}</ref>


<ref name="NAMS 1996">{{cite journal|url=http://www.ams.org/notices/199610/comm-shapiro.pdf |last=Shapiro |first=Daniel B. |title=A Conference Honoring Arnold Ross on His Ninetieth Birthday |date=October 1996 |journal=[[Notices of the American Mathematical Society]] |publisher=[[American Mathematical Society]] |issn=0002-9920 |volume=43 |issue=10 |pages=1151–1154 |accessdate=September 14, 2013 |archiveurl=https://web.archive.org/web/20130722010627/http://www.ams.org/notices/199610/comm-shapiro.pdf |archivedate=July 22, 2013 |deadurl=no |df= }}</ref>
<ref name="NAMS 1996">{{cite journal|url=https://www.ams.org/notices/199610/comm-shapiro.pdf |last1=Shapiro |first1=Daniel B. |title=A Conference Honoring Arnold Ross on His Ninetieth Birthday |date=October 1996 |journal=[[Notices of the American Mathematical Society]] |publisher=[[American Mathematical Society]] |issn=0002-9920 |volume=43 |issue=10 |pages=1151–1154 |access-date=September 14, 2013 |archive-url=https://web.archive.org/web/20130722010627/http://www.ams.org/notices/199610/comm-shapiro.pdf |archive-date=July 22, 2013 |url-status=live }}</ref>


<ref name="NAMS 1998">{{cite journal|url=http://www.ams.org/notices/199804/comm-cit-pubserv.pdf |title=1998 Citations for Public Service |date=April 1998 |journal=[[Notices of the American Mathematical Society]] |publisher=[[American Mathematical Society]] |issn=0002-9920 |volume=45 |issue=4 |pages=514–516 |accessdate=September 20, 2013 |archiveurl=https://web.archive.org/web/20121202115433/http://www.ams.org/notices/199804/comm-cit-pubserv.pdf |archivedate=December 2, 2012 |deadurl=no |df= }}</ref>
<ref name="NAMS 1998">{{cite journal|url=https://www.ams.org/notices/199804/comm-cit-pubserv.pdf |title=1998 Citations for Public Service |date=April 1998 |journal=[[Notices of the American Mathematical Society]] |publisher=[[American Mathematical Society]] |issn=0002-9920 |volume=45 |issue=4 |pages=514–516 |access-date=September 20, 2013 |archive-url=https://web.archive.org/web/20121202115433/http://www.ams.org/notices/199804/comm-cit-pubserv.pdf |archive-date=December 2, 2012 |url-status=live }}</ref>


<ref name="NAMS 2001">{{cite journal|url=http://www.ams.org/notices/200107/fea-ross.pdf |last=Jackson |first=Allyn |title=Interview with Arnold Ross |date=August 2001 |journal=[[Notices of the American Mathematical Society]] |publisher=[[American Mathematical Society]] |issn=0002-9920 |volume=48 |issue=7 |pages=691–698 |accessdate=September 14, 2013 |archiveurl=https://web.archive.org/web/20130921104120/http://www.ams.org/notices/200107/fea-ross.pdf |archivedate=September 21, 2013 |deadurl=no |df= }}</ref>
<ref name="NAMS 2001">{{cite journal|url=https://www.ams.org/notices/200107/fea-ross.pdf |last1=Jackson |first1=Allyn |title=Interview with Arnold Ross |date=August 2001 |journal=[[Notices of the American Mathematical Society]] |publisher=[[American Mathematical Society]] |issn=0002-9920 |volume=48 |issue=7 |pages=691–698 |access-date=September 14, 2013 |archive-url=https://web.archive.org/web/20130921104120/http://www.ams.org/notices/200107/fea-ross.pdf |archive-date=September 21, 2013 |url-status=live }}</ref>


<ref name="NAMS 2003">{{cite journal|url=http://www.ams.org/notices/200306/comm-ross.pdf |title=Arnold Ross (1906–2002) |editor-last1=Jackson |editor-first1=Allyn |editor-last2=Shapiro |editor-first2=Daniel |date=June–July 2003 |journal=[[Notices of the American Mathematical Society]] |publisher=[[American Mathematical Society]] |issn=0002-9920 |volume=50 |issue=6 |pages=660–665 |accessdate=September 14, 2013 |archiveurl=https://web.archive.org/web/20130722010454/http://www.ams.org/notices/200306/comm-ross.pdf |archivedate=July 22, 2013 |deadurl=no |df= }}</ref>
<ref name="NAMS 2003">{{cite journal|url=https://www.ams.org/notices/200306/comm-ross.pdf |title=Arnold Ross (1906–2002) |editor-last1=Jackson |editor-first1=Allyn |editor-last2=Shapiro |editor-first2=Daniel |date=June–July 2003 |journal=[[Notices of the American Mathematical Society]] |publisher=[[American Mathematical Society]] |issn=0002-9920 |volume=50 |issue=6 |pages=660–665 |access-date=September 14, 2013 |archive-url=https://web.archive.org/web/20130722010454/http://www.ams.org/notices/200306/comm-ross.pdf |archive-date=July 22, 2013 |url-status=live }}</ref>


<ref name="OSU 2002">{{cite web|url=http://www.math.osu.edu/news/2002/ross_1906-2002.html |accessdate=September 20, 2013 |title=Arnold Ross 1906–2002 |last1=Shapiro |first1=Daniel |date=September 25, 2002 |publisher=[[Ohio State University|Ohio State University Department of Mathematics]] |archiveurl=https://web.archive.org/web/20130921061110/http://www.math.osu.edu/news/2002/ross_1906-2002.html |archivedate=September 21, 2013 |deadurl=no |df= }}</ref>
<ref name="OSU 2002">{{cite web|url=http://www.math.osu.edu/news/2002/ross_1906-2002.html |access-date=September 20, 2013 |title=Arnold Ross 1906–2002 |last1=Shapiro |first1=Daniel |date=September 25, 2002 |publisher=[[Ohio State University|Ohio State University Department of Mathematics]] |archive-url=https://web.archive.org/web/20130921061110/http://www.math.osu.edu/news/2002/ross_1906-2002.html |archive-date=September 21, 2013 |url-status=live }}</ref>


<ref name="OSU obituary">{{cite web|url=http://www.math.osu.edu/news/2002/ross_obituary.html |accessdate=September 20, 2013 |title=Arnold Ross Obituary |year=2002 |publisher=[[Ohio State University|Ohio State University Department of Mathematics]] |archiveurl=https://web.archive.org/web/20130921061121/http://www.math.osu.edu/news/2002/ross_obituary.html |archivedate=September 21, 2013 |deadurl=no |df= }}</ref>
<ref name="OSU obituary">{{cite web|url=http://www.math.osu.edu/news/2002/ross_obituary.html |access-date=September 20, 2013 |title=Arnold Ross Obituary |year=2002 |publisher=[[Ohio State University|Ohio State University Department of Mathematics]] |archive-url=https://web.archive.org/web/20130921061121/http://www.math.osu.edu/news/2002/ross_obituary.html |archive-date=September 21, 2013 |url-status=live }}</ref>


<!--<ref name="PNAS">{{cite journal | vauthors = Ross AE | title = On Representation of Integers by Quadratic Forms | journal = Proceedings of the National Academy of Sciences of the United States of America | volume = 18 | issue = 9 | pages = 600–8 | date = September 1932 | pmid = 16577482 | doi=10.1073/pnas.18.9.600 | pmc=1076292}}</ref>-->
<!--<ref name="PNAS">{{cite journal | vauthors = Ross AE | title = On Representation of Integers by Quadratic Forms | journal = Proceedings of the National Academy of Sciences of the United States of America | volume = 18 | issue = 9 | pages = 600–8 | date = September 1932 | pmid = 16577482 | doi=10.1073/pnas.18.9.600 | pmc=1076292}}</ref>-->


<ref name="RNAS">{{cite book|author=National Academy of Sciences (U.S.)|authorlink=National Academy of Sciences|title=Report of the National Academy of Sciences|url=https://books.google.com/books?id=x04rAAAAYAAJ&pg=RA4-PA164|year=1930|publisher=[[United States National Academies]]|page=164|id=NAP:11240}}</ref>
<ref name="RNAS">{{cite book|author=National Academy of Sciences (U.S.)|author-link=National Academy of Sciences|title=Report of the National Academy of Sciences|url=https://books.google.com/books?id=x04rAAAAYAAJ&pg=RA4-PA164|year=1930|publisher=[[United States National Academies]]|page=164|id=NAP:11240}}</ref>


<ref name="Wissner-Gross 2007">{{cite book|last=Wissner-Gross|first=Elizabeth|title=What High Schools Don't Tell You: 300+ Secrets to Make Your Kid Irresistible to Colleges by Senior Year|url=https://books.google.com/books?id=xJ9YU2Hj71AC&pg=PA103|accessdate=September 20, 2013|year=2007|publisher=Hudson Street Press|isbn=978-1-59463-037-8|pages=103–109}}</ref>
<ref name="Wissner-Gross 2007">{{cite book|last1=Wissner-Gross|first1=Elizabeth|title=What High Schools Don't Tell You: 300+ Secrets to Make Your Kid Irresistible to Colleges by Senior Year|url=https://archive.org/details/whathighschoolsd0000wiss|url-access=registration|access-date=September 20, 2013|year=2007|publisher=Hudson Street Press|isbn=978-1-59463-037-8|pages=[https://archive.org/details/whathighschoolsd0000wiss/page/103 103]–109}}</ref>


<ref name=Zassenhaus>{{cite journal|last=Pohst|first=Michael|title=In Memoriam: Hans Zassenhaus (1912–1991)|journal=[[Journal of Number Theory]]|volume=47|issue=1|date=April 1994|issn=0022-314X|page=11|via=[[ScienceDirect|ScienceDirect Mathematics Backfile]]|doi=10.1006/jnth.1994.1023}}</ref>
<ref name=Zassenhaus>{{cite journal|last1=Pohst|first1=Michael|title=In Memoriam: Hans Zassenhaus (1912–1991)|journal=[[Journal of Number Theory]]|volume=47|issue=1|date=April 1994|issn=0022-314X|page=11|via=[[ScienceDirect|ScienceDirect Mathematics Backfile]]|doi=10.1006/jnth.1994.1023|doi-access=free}}</ref>


}}
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[[Category:20th-century American mathematicians]]
[[Category:21st-century American mathematicians]]
[[Category:21st-century American mathematicians]]
[[Category:Saint Louis University mathematicians]]
[[Category:American people of Ukrainian-Jewish descent]]
[[Category:American people of Ukrainian-Jewish descent]]
[[Category:Ohio State University faculty]]
[[Category:Ohio State University faculty]]

Latest revision as of 03:15, 14 August 2024

For the American jazz musician, see Arnold Ross (musician).
Arnold Ephraim Ross
Arnold Ross in his later years with combed-back white and gray hair, exposed forehead, and wearing a jacket in front of a green chalkboard
Ross in 1970
Born
Arnold Ephraim Chaimovich

(1906-08-24)August 24, 1906
Chicago, Illinois, US
DiedSeptember 25, 2002(2002-09-25) (aged 96)
Alma materUniversity of Chicago
Known forMathematics education
(Ross Mathematics Program)
Spouse(s)Bertha (Bee) Halley Horecker
Madeleine Green
Scientific career
FieldsNumber theory
InstitutionsCalifornia Institute of Technology, St. Louis University, University of Notre Dame, Ohio State University
Thesis"On Representation of Integers by Indefinite Ternary Quadratic Forms of Quadratfrei Determinant" (1931)
Doctoral advisorL. E. Dickson
Other academic advisorsSamuil Shatunovsky,
E. H. Moore
Doctoral studentsMargaret Willerding

Arnold Ephraim Ross (August 24, 1906 – September 25, 2002) was a mathematician and educator who founded the Ross Mathematics Program, a number theory summer program for gifted high school students. He was born in Chicago, but spent his youth in Odesa, Ukraine, where he studied with Samuil Shatunovsky. Ross returned to Chicago and enrolled in University of Chicago graduate coursework under E. H. Moore, despite his lack of formal academic training. He received his Ph.D. and married his wife, Bee, in 1931.

Ross taught at several institutions including St. Louis University before becoming chair of University of Notre Dame's mathematics department in 1946. He started a teacher training program in mathematics that evolved into the Ross Mathematics Program in 1957 with the addition of high school students. The program moved with him to Ohio State University when he became their department chair in 1963. Though forced to retire in 1976, Ross ran the summer program until 2000. He had worked with over 2,000 students during more than forty summers.

The program is known as Ross's most significant work. Its attendees have since continued on to prominent research positions across the sciences. His program inspired several offshoots and was recognized by mathematicians as highly influential. Ross has received an honorary doctorate and several professional association awards for his instruction and service.

Early life and career

[edit]
Ross as young boy in school uniform

Ross was born Arnold Ephraim Chaimovich[1] on August 24, 1906, in Chicago to Ukrainian-Jewish immigrants.[2] He was an only child.[1] His mother supported the family as a physical therapist.[1] Ross returned to Odesa, Ukraine with his mother in 1909 for assistance from her extended family,[1] and stayed once World War I and the Russian Revolution broke out.[2] The two events led to widespread famine and economic woe in the region.[1] Ross learned Russian at the behest of his mother, and developed a love of the theater and language.[1] Ross's mother encouraged him to read, which he did often, and subscribed to a private library since Odesa had no public library.[1] He credited his favorite uncle, an X-ray diagnostician, with introducing him to mathematics.[1] The uncle had hired Samuil Shatunovsky to tutor his talented son, and Ross asked to join in.[1] As money meant little due to inflation, Shatunovsky was paid to tutor the two boys with a pound of French hard candy.[1] During this time, Ross was not taught with textbooks or lectured on geometric proofs.[1] His geometry teacher would ask the class to prove and justify ideas on the blackboard per trial and error.[1] Many universities were closed due to the famine, but Odesa University reopened and let a small group of adolescents attend, including Ross.[1]

Ross in Odesa circa 1922

Ross left Odesa—now part of Ukraine—in 1922 with the intention of returning to Chicago and studying topology with E. H. Moore at the University of Chicago.[1] After negotiating his way home, he worked at a family friend's bookbinding shop and continued to learn English at the Lewis Institute.[1] He also changed his surname from Chaimovich to Ross in 1922.[3] Ross used his salary from a year at the shop to enroll for one term at the University of Chicago in Moore's course.[1] Moore gave Ross special attention, knowing his untraditional background, and arranged for Ross to attend the topology class as the sole undergraduate.[1]

In Moore's teaching style, he would propose a conjecture and task the students with proving it.[1] Students could respond with counter-conjectures that they would defend.[1] Ross found Moore's method exciting,[1] and his pedagogy influenced Ross's own.[2] Ross graduated with a B.S. degree[4] and continued his study as Leonard Eugene Dickson's research assistant.[2] Ross earned a M.S. degree[4] and finished his Ph.D. in number theory at the University of Chicago in 1931 with Dickson as his adviser.[2] Ross's dissertation was entitled "On Representation of Integers by Indefinite Ternary Quadratic Forms".[1] He did not pay tuition after his first quarter, which he credits to Dickson.[1]

Ross married Bertha (Bee) Halley Horecker, a singer-musician and daughter of Ross's Chicago neighbors, in 1931,[1] received a National Research Council Fellowship for 1932,[5] and worked as a National Research Council postdoctoral fellow[4] at California Institute of Technology with Eric Temple Bell until 1933.[2] Ross moved back to Chicago and led the mathematics department at an experimental school started by Ph.D.s during the Great Depression, People's Junior College,[4] where he also taught physics.[1] Ross became an assistant professor at St. Louis University in 1935 and stayed for about 11 years.[2] In an interview, he said he advocated for a student who became the first black woman in the South to receive a master's degree in mathematics.[1] This exception led the university to admit black students despite the idea's widespread unpopularity.[1] During World War II, Ross served as a research mathematician for the U.S. Navy.[2] He befriended Hungarian mathematician Gábor Szegő while in St. Louis, who recommended Ross for a 1941 Brown University summer school that prepared young scientists to assist in the war, a program Ross attended.[1] He occasionally worked on proximity fuzes for Stromberg-Carlson's laboratory from 1941 to 1945[1] before accepting a position as head of University of Notre Dame's mathematics department in 1946.[2] He set out to change the school's research climate by inviting distinguished mathematicians including Paul Erdős, whom Ross made a full professor.[1]

Ross Mathematics Program

[edit]

While at Notre Dame in 1947, Ross began a mathematics program that prioritized what he described as "the act of personal discovery through observation and experimentation" for high school and junior college teachers.[1] In 1957, the program expanded via the National Science Foundation's post-Sputnik funds for teacher retraining, and Ross let high school students attend.[1] This expansion became the Ross Mathematics Program,[1] a summer mathematics program for talented high school students.[2] The program lasts eight weeks and brings students with no prior knowledge to topics such as Gaussian integers and quadratic reciprocity.[2] Though the program teaches number theory, by its Gauss-inspired[6] motto, "Think deeply of simple things," its primary goal is to offer precollege students an intellectual experience[2] as what he described as "a vivid apprenticeship to a life of exploration."[1][7] The program is known for its intensity, and is considered America's "most rigorous number theory program."[8] Ross was known to say, "No one leaves the program unchanged."[9]

This emphasis on computation alone too often produces students who have never practiced thinking for themselves, who have never asked why things work the way they do, who are not prepared to lead the way to future scientific innovation. It is precisely this independence of thought and questioning attitude that the Ross Program strives to nurture.

Ross Program brochure[8]

The program usually has 40–50 first-year students, 15 junior counselors, and 15 counselors.[2] Students are admitted by application—which includes a set of mathematical questions—or by showing "a great eagerness to learn."[2] First-year students meet daily for lectures in elementary number theory and thrice weekly for problem seminars.[2] They are encouraged to think like scientists and devise their own proofs and conjectures to the problems posed,[2] which occupies most of their free time.[8] Ross designed the daily problem sets,[9] and many questions contain his signature directions: "Prove or disprove and salvage if possible."[1] Successful students are asked to return as junior counselors and counselors in future summers.[2] Junior counselors revisit the daily lectures and help first-years with their questions.[2] They also can take advanced courses such as combinatorics[2] and graduate seminars.[9] Student problem sets are graded daily by the live-in counselors.[2]

The program was funded in the 1960s by a National Science Foundation (NSF) program that supported summer programs in science education, but not returning students.[2] As NSF support fluctuates, the program has been funded by various means including gifts from donors, scholarships from businesses, a National Security Agency grant, the university, and its mathematics department.[2] It also receives financial support from the Clay Mathematics Institute.[1][8]

The program grew rapidly with input from prominent mathematicians such as Ram Prakash Bambah, Hans Zassenhaus, Thoralf Skolem, and Max Dehn.[2] In the 1960s and 1970s, Ross brought mathematicians including Zassenhaus, Kurt Mahler, and Dijen K. Ray-Chaudhuri to teach there regularly.[1] Ross left Notre Dame to become chair of Ohio State University's mathematics department in 1963, and the program followed in the 1964 summer.[2] The program briefly moved to the University of Chicago in the summers of 1975–1978 at mathematician Felix Browder's invitation.[2] The program is unadvertised and depends on personal contacts and word of mouth to propagate.[1][2][8] It is recognized by mathematicians as one of the best mathematics programs for high school students.[8]

Admission to the program is competitive, with an approximately 15% acceptance rate. [10]

Retirement and death

[edit]

Ross reached his mandatory retirement from Ohio State University in 1976,[2] when he became Professor Emeritus,[4] but continued to run the summer program through 2000,[9] after which he had a stroke that left him physically impaired and unable to teach.[1] Daniel Shapiro led the program upon Ross's exit.[1][11] Shapiro was a former counselor at the program.[3]

Ross received an honorary doctorate from Denison University in 1984,[4] the 1985 Mathematics Association of America (MAA) Award for Distinguished Service,[2] the 1998 MAA Citation for Public Service,[7] and was named an American Association for the Advancement of Science Fellow in 1988.[2] His teaching awards include Ohio State's Distinguished Teaching and Service Awards, and membership on the National Science Foundation's science education advisory board.[4]

Ross helped begin similar programs in West Germany, India, and Australia.[2] He consulted for an Indian gifted children program in 1973, assisted in an Australian National University January summer program for talented youth based on Ross's own from 1975 to 1983, and helped start another program in Heidelberg, Germany in 1978.[4] He had previously created other mathematics programs, including the teacher training program (before it included high school students)[1] and another program for Columbus, Ohio inner city middle and high school students called "Horizons Unlimited" in 1970.[4]

Ross's wife, Bee, died in 1983 and left Ross in a deep depression.[1] His colleagues said he "lived only for his summer program" in this period.[1] He later met a French widow of a diplomat, Madeleine Green, and they married in 1990.[1]

Ross died on September 25, 2002.[12] Notices of the American Mathematical Society and MAA FOCUS ran memorial articles on Ross.[3][9][12] Mathematicians such as Karl Rubin expressed their personal debts to Ross.[3] He did not have any children.[2][13]

Legacy

[edit]

Ross's biggest contribution to his field was not through his research, but through his mathematics education programs.[9] He had run each of his summer programs from 1957 to 2000,[9] working with over 2,000 students.[1] His summer program graduates found roles in prestigious research positions in fields across the sciences.[9] The Ross Program was acclaimed by mathematicians as highly influential.[8][9][14]

The Ross Program inspired many similar programs, the closest in likeness being the Program in Mathematics for Young Scientists (PROMYS) at Boston University and the Honors Math Camp at Southwest Texas State University.[1] Other programs at University of Chicago and University of Texas at San Antonio were inspired by Ross.[1] The founders of PROMYS were Ross Program alumni,[8] and when the Ross Program went to the University of Chicago for several years, mathematics chair Paul Sally slowly became supportive of the program and later began his own gifted students program.[1] Informally, Ross Program and Ross's students are known as "Ross-1s" and those who study under them (including PROMYS attendees) are known as "Ross-2s".[8]

The Arnold Ross Lecture Series founded in his name in 1993[13] and run by the American Mathematical Society puts mathematicians before high school audiences annually in cities across the United States.[1] Ohio State University organized two reunion-conferences for Ross with program alumni, friends of Ross, and a series of science lectures,[1] in 1996 and 2001.[15]

References

[edit]
  1. ^ a b c d e f g h i j k l m n o p q r s t u v w x y z aa ab ac ad ae af ag ah ai aj ak al am an ao ap aq ar as at au av aw Jackson, Allyn (August 2001). "Interview with Arnold Ross" (PDF). Notices of the American Mathematical Society. 48 (7). American Mathematical Society: 691–698. ISSN 0002-9920. Archived (PDF) from the original on September 21, 2013. Retrieved September 14, 2013.
  2. ^ a b c d e f g h i j k l m n o p q r s t u v w x y z aa ab ac ad ae Shapiro, Daniel B. (October 1996). "A Conference Honoring Arnold Ross on His Ninetieth Birthday" (PDF). Notices of the American Mathematical Society. 43 (10). American Mathematical Society: 1151–1154. ISSN 0002-9920. Archived (PDF) from the original on July 22, 2013. Retrieved September 14, 2013.
  3. ^ a b c d Jackson, Allyn; Shapiro, Daniel, eds. (June–July 2003). "Arnold Ross (1906–2002)" (PDF). Notices of the American Mathematical Society. 50 (6). American Mathematical Society: 660–665. ISSN 0002-9920. Archived (PDF) from the original on July 22, 2013. Retrieved September 14, 2013.
  4. ^ a b c d e f g h i Lax, Anneli; Woods, Alan C. (April 1986). "Award for Distinguished Service to Professor Arnold Ephraim Ross". American Mathematical Monthly. 93 (4). Mathematical Association of America: 245–246. doi:10.1080/00029890.1986.11971798. ISSN 0002-9890. JSTOR 2323671.
  5. ^ National Academy of Sciences (U.S.) (1930). Report of the National Academy of Sciences. United States National Academies. p. 164. NAP:11240.
  6. ^ William C. Bauldry (9 September 2011). Introduction to Real Analysis: An Educational Approach. John Wiley & Sons. p. 46. ISBN 978-1-118-16443-3. Retrieved September 20, 2013.
  7. ^ a b "1998 Citations for Public Service" (PDF). Notices of the American Mathematical Society. 45 (4). American Mathematical Society: 514–516. April 1998. ISSN 0002-9920. Archived (PDF) from the original on December 2, 2012. Retrieved September 20, 2013.
  8. ^ a b c d e f g h i Wissner-Gross, Elizabeth (2007). What High Schools Don't Tell You: 300+ Secrets to Make Your Kid Irresistible to Colleges by Senior Year. Hudson Street Press. pp. 103–109. ISBN 978-1-59463-037-8. Retrieved September 20, 2013.
  9. ^ a b c d e f g h i Stevens, Glenn (January 2003). "Memories of Arnold Ross" (PDF). MAA FOCUS. 23 (1). Mathematical Association of America: 17. ISSN 0731-2040. Archived (PDF) from the original on September 21, 2013. Retrieved September 20, 2013.
  10. ^ "Frequently Asked Questions". The Ross Mathematics Program. Retrieved 22 October 2023.
  11. ^ Edgar, Gerald A. (October 23, 2007). Measure, Topology, and Fractal Geometry. Springer-Verlag. p. XI. ISBN 978-0-387-74749-1. Retrieved September 20, 2013.
  12. ^ a b Stevens, Glenn (December 2002). "Memories of Arnold Ross" (PDF). MAA FOCUS. 22 (9). Mathematical Association of America: 22. ISSN 0731-2040. Archived (PDF) from the original on September 21, 2013. Retrieved September 20, 2013.
  13. ^ a b "Arnold Ross Obituary". Ohio State University Department of Mathematics. 2002. Archived from the original on September 21, 2013. Retrieved September 20, 2013.
  14. ^ Pohst, Michael (April 1994). "In Memoriam: Hans Zassenhaus (1912–1991)". Journal of Number Theory. 47 (1): 11. doi:10.1006/jnth.1994.1023. ISSN 0022-314X – via ScienceDirect Mathematics Backfile.
  15. ^ Shapiro, Daniel (September 25, 2002). "Arnold Ross 1906–2002". Ohio State University Department of Mathematics. Archived from the original on September 21, 2013. Retrieved September 20, 2013.
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