Which of the following generalizations seem to be true when we compare and contrast paper 1 mathematicians (women and minorities in the 18th and 19th centuries) to paper 2 mathematicians (women and minorities born between 1900 and 1925 to paper 3 mathematicians (women and minorities born after 1925)

1. In paper 1, all but one of the women we studied were unmarried (and the married woman had gotten married in order to travel and obtain an education). In paper 2, most of the women we studied were married, and some had children. In paper 3, we continue to see successful women mathematicians who are are married, have children, and are great mathematicians. It seems as time is progressing, women are better able to balance a career with family, although being able to achieve a good balance remains a concern of women mathematicians today.
2. Fifty percent of the women that we studied in paper 2 were married to mathematicians, and so they would have been subject to nepotism rules. During the day that Dr. Hirst visited, it was also true that fifty percent of the women mathematicians present were married to mathematicians. In paper 3, we continue to see a high percentage of women mathematicians married to mathematicians. While we do not expect this to be the percentage in general, it makes sense that many woman mathematicians have married male mathematicians, since their social circle would often consist of many mathematicians and scientists. Studies have backed up this phenomenon. Of course on the day that Dr. Kirsty Flemming and Dr. Jill Richie came to visit, 0% of the women mathematicians were married to mathematicians. The studies that back up the phenomenon study statistically significant groups of women mathematicians.
3. In paper 1, the two African Americans with PhDs ended up with positions at Howard University, and it is still true in paper 2 that most of the African American mathematicians ended up with positions at traditionally Black institutions. In paper 3, we see African American mathematicians working at many different types of institutions.
4. In paper 1, African American mathematicians and women seemed to be oddities in the sense that there were so few of them. The numbers of African American and women mathematicians have increased greatly as time has progressed. Part of this increase is probably due to increased educational opportunities.
5. We have seen numerous examples of blatent gender and racial discrimination in papers 1, 2 and 3.
6. More recently, we have also seen and heard about numerous examples of subtle gender or racial discrimination that can be just as devastating as overt discrimination.
7. Most of the mathematicians that we studied had a good support system from family and/or mentors, which seems to have been important to help them overcome other barriers.
8. We have seen that teachers (male or female) can make a big difference in someone's career at any stage of the educational process.

Which of the following are true based on Richard Tapia and his mathematics?

1. Richard Tapia is a successful mathematician, who has had the support of family and peers. Yet, he still faces racial descrimination as a Hispanic.
2. In school, the counselors had low expectations and did not give advice on how to obtain the best education. For example, he was not been advised in high school that he could attend a four-year college such as the University of California, even though his grades were good enough. Instead, he first went to a junior college.
3. Tapia was working with complicated des. He wanted to know about them and find their max/mins. This is equivalent to finding a root of the derivative (ie where the derivative is 0), so a version of the Newton method called the weak Newton method is used.
4. Newton's method of approximation is really the tangent line approximation used to find a zero of a function.
5. Given f1(x,y)=3x^2+4y^2-1, and f2(x,y)=y^3-8x^3-1, the Wronskian at a point (x,y) is equal to 18xy^2 + 24*x^2y.
6. Given f1(x,y)=3x^2+4y^2-1, and f2(x,y)=y^3-8x^3-1, the Wronskian at the point (-.5,.25) is 11.4375.
7. Given f1(x,y)=3x^2+4y^2-1, and f2(x,y)=y^3-8x^3-1, and the point (-.5, .25), the zero is approximated by Newton's method to be located at (-.497,.254).

Which of the following are true based on Doris Schattschneider and her mathematics?

1. Doris' parents had high educational expectations for their children, and her high school mathematic's teacher also encouraged her.
2. The definition of distance in taxicab geometry is |x2-x1| + |y2-y1|. The distance between (0,0) and (1,1) is sqrt(2).
3. She was looking at transformations that preserve the taxicab distance between points and proved that there were only 8 of them.
4. Taxicab geometry is useful for taxicab drivers in a city set on a grid and also for ecological distance between species.
5. SAS does not hold in taxicab geometry because we can draw two right triangles that have two sides and the angle between them congruent, but whose last side is different, as follows:
Take triangle 1 as being formed by the three points (0,0), (0,2) and (4,0). This is a right triangle, with one base 2, height 4, and hypotenuse 6 (with lenghts measured in the taxicab distance formula).
Take triangle 2 with points at (1,1), (0,2), and (3,3). Then this is a right triangle with base 2, height 4, and hypotenuse 4.
Since the hypotenuses have different lenghts, then these two triangles violated SAS.

Which of the following are true based on Jean Taylor and her mathematics?

1. Her first experience with blatant sexism was in high school where a male student told her it was not fair that she received higher marks than he did, for he needed better grades for his "career".
2. She attended a women's college, Mount Holyoke, before enrolling at UC Berkeley. There, was was encouraged by her boyfriend to audit graduate level mathematics courses. She later married her boyfriend, who was also a mathematician.
3. She worked onsoap bubble geometry - the geometry of minimal surfaces. These have applications in chemistry, biology and packaging
4. One of the things that she proved was that three surfaces meet along a smooth curve at 130 degree angles.
5. The mean curvature of the origin of a saddle surface is 0.
6. The mean curvature of any soap bubble surface is constant.
7. A spherical bubble has the least amount of surface area for a given volume

Which of the following are true based on Fan Chung Graham and her mathematics?

1. Fan Chung said: As an undergraduate in Taiwan, I was surrounded by good friends and many women mathematicians. We enjoyed talking about mathematics and helping each other. A large part of education is learning from your peers, not just the professors. Seeing other women perform well is a great confidence builder, too!
2. She had encouragement from her parents. Her mother encouraged Fan to have a career and "not just to be an attachment to a man." While her husband is a mathematician, she is certainly not just an attachment to him!
3. One of the many papers whe has written is on the mathematics of a BuckyBall. A Buckyball is a molecule comprised of 60 carbon atoms arranged in a form similar to a soccer ball, and that mathematical properties have applications to chemisty and physics.
4. Euler's formula is true for all figures. It says that the vertices minus the edges plus the faces are always 2.
5. A Buckyball satisfies Euler's formula, as it has 60 vertices, 90 edges and 32 faces.

Which of the following are true based on Carolyn Gordon and her mathematics?

1. Only 25-30% of the PhDs awarded annually go to women in mathematics. Since a higher percentage of Carolyn Gordon's students are women, this indicates that she appeals to women who want to become mathematicians.
2. At one point while Carolyn Gordon and her husband, mathematician David Webb, were working to find their drums, they filled up their living room with huge paper models.
3. Two drums that sound the same must have the same area and perimeter. For example, a larger area drum has a lower tone, so one can hear this difference.
4. Two circular drums of different sizes can never have the same sound. A square and a circular drum can never have the same sound.
5. In their proof, they found two drums that sounded the same but had different shapes. They did not play their drums to prove that they had the same sound. Instead, they proved this mathematically. But, some physicists tested this out and found that they did sound the same within an error that was within the experimental error range.

Which of the following are true based on Freeman Hrabowski and his mathematics?

1. Freeman peeled off the paper cover of his tattered second-grade textbook and discovered the original cloth cover, which was stamped with the name of the white school across town. A cast-off. A teacher told the dismayed child, don't worry about the book, just "get the knowledge and you'll be fine."
2. The little boy who was subjected to extreme racism has achieved more than just "getting the knowledge". He has grown up to be the President of a nationally known university, and has overcome great obstacles and encouraged hundereds of minority students.
3. An F-test is used for testing numerical data, not the percentage or proportions of a sample for a particular category.
4. A better test for analyzing proportional data is a chi-squared test.
5. If my column looks like the following
[Group                          Graduated    Not Graduated   Total]
[(Students from black colleges)   24   39   63  ]
[(Students from white colleges)   10    30    40  ]
[Total                                          34    69    103   ]
then the expected value of the first row, first column is 20.80.
6. To find the expected value of students from traditionally Black colleges who graduated, I would take the total number of students from traditionally Black colleges, multiply by the total number of students that graduated in my study, and divide by the total number of students who graduated in my study.
The expected value measures the number of students you would expect to see if graduation rates do NOT depend on whether you attended a historically Black college or not.
7. Using the chi-squared test on the table, we found that there was not a significant difference in the proportions from the different type of schools. Hrabowski came to the same conclusion with the F-test, but using the F-test could have led him to a different conclusion.
8. Just like in mathematics, where we must prove statements before using them, in statistics, there are theorists who work out accepted techniques. Many of the techniques are the same as our intuition. For example, we could just throw out some of our sample participants in order to equalize the numbers in each category.
9. It seems that Hrabowski has matured statistically from his 1977 article "Graduate School Success of Black Students from White Colleges and Black Colleges" to his 1995 article "Enhancing the Success of African-American Students in the in the Sciences: Freshmen Year Outcomes".

Which of the following are true based on Nathaniel Dean and his mathematics?

1. According to the Mathematicians of the African Diaspora web pages, Nathaniel Dean is one of the select outstanding African American researchers who shows a lot of promise for becoming one of the greatest African American mathematicians in the field of mathematics.
2. Graph theory has no applications to real life.
3. A hexagon is a cycle. Walking the shortest distance from Walker hall to the gym forms a path, not a cycle.
4. In one of Dean's papers, a lemma that he proves discusses the number of paths it takes in order to decompose a graph made up of 1 , 2 or 3 cycles. Decomposition of a graph can be useful, since it is easier to work with smaller pieces.
5. His proof of the lemma is by contradiction.

Which of the following are true based on Karen Smith and her mathematics?

1. Although she always loved mathematics and wanted to be a mathematician from a young age, she did not realize that one could have a career as a mathematician until college, when her freshman calculus teacher, Professor Charles Fefferman, suggested it.
2. While continuing her mathematical career, she encountered many people (men and women) who seemed to discourage her and her work seemingly because she was a woman.
3. Characteristic p says that a ring R has a positive integer p so that a+a+...+a=0 for every element in the ring (where we add each element to itself p times). If no p exists than the ring has characteristic 0.
4. Z_3 has characteristic 0. 2+2+2=0 mod 3.
5. If you are looking for solutions to an equation, as in Fermat's Last Theorem, sometimes it is useful to reduce mod p, and work in characteristic p. This is because there would be only finitely many numbers to work with, and solving the equation in characteristic p can help to give intuition about the original probelm.

Which of the following are true based on Jonathan Farley and his mathematics?

1. Jonathan Farley did not decide to become a mathematics professor until he was fourteen years old. In his tenth grade English class, he had a questionnaire that would help determine vocation. He was told to become a mathematician or statistician.
2. Farley is interested in African history, politics and philosophy in additon to mathematics. Two of his heros are Dr. Huey P. Newton, co-founder of teh Black Panther Party, and Frantz Fanon, author of The Wretched of the Earth.
3. His area of research is lattice theory, which deals with partially ordered sets so that any two elements have a least upper bound and a greatest lower bound. Lattices have many applications, including applications to cryptography.
4. If I have two points 1 and 2, with no lines connecting them, then 1 and 2 do not have an upper bound, since there is nothing bigger than both of them at once, so this is not a lattice.
5. If I have 4 points 1, 2, 3 and 4, with 1 and 2 on the bottom, and 3 and 4 on the top (say the corners of a square, with 1 bottom left, and 3 top left). And also the following lines: 1 is connected to 3 and 4. 2 is connected to 3 and 4. (No other line connections). Then this is a partially ordered set that is not a lattice since 1 and 2 have no LEAST upper bounds. 3 and 4 are both upper bounds, but there is no ordering of 3 compared to 4, so we have no way of saying that one is smaller or larger than the other