# More 3 Student's Book 55

Did you know that you can fit more water drops on a penny than you might think? This simple experiment is a fun and easy way to learn about the surface tension of water. All you need is a penny and some water.

## more 3 student's book 55

According to the NEA Survey, three-fourths of members said they've had to fill in for colleagues or take other duties due to these shortages. Furthermore, 80 percent report that unfilled job openings have led to more work obligations for the educators who remain.

When asked about potential ways to address the issue, respondents pointed to higher salaries, providing additional mental supports for students, hiring more teachers, hiring more support staff, and less paperwork.

The survey also asked respondents about COVID's ongoing impact on their schools. Even amidst the Omicron surge, more than a third of educators say mask and mitigation policies have been eased since the beginning of the 2021-22 school year. Inadequate ventilation remains a top concern. Only 38 percent of educators reported having improved ventilation in their schools and only 28 percent believe their school's ventilation system provides them with enough protection.

You can expect to see students bailing from Math 55 on a regular basis. The class size shrinks to half its original size or less before the semester is over. According to one student who took Math 55 in 2005, and kept a running tally of attendance, "We had 51 students the first day, 31 students the second day, 24 for the next four days, 23 for two more weeks, and then 21 for the rest of the first semester after the fifth Monday.

In Williams' book, he describes Richard Stallman's Math 55 ending the semester with 20 students, eight of whom would go on to become future mathematics professors. One eventually went on to teach physics.

Those who enroll in Math 55 might wonder whether they are actually able to handle it. Well, it becomes clear pretty quick, thanks to a diagnostic exam for enrollees. Students scoring more than 50 percent are encouraged to enroll in Math 55, while those who score less than 10 percent are advised to take Math 21. If you fall in between, the choice is yours.

According to the freshman guide, Math 55 "often contains former members of the International Math Olympiad teams." That's the worldwide championship competition in which high school math students from more than 100 countries go head-to-head on ridiculously tough math problems.

Professor Yum-Tong Siu, whose class began with 50 students in 2003, said he actively tried to whittle down the class size. As The Harvard Independent reports, the class dropped down to 25 students, but Siu added: "I want to reduce it a bit more." The goal: 20. "We want a group of students with similar backgrounds so we can proceed at a pace that can suit them at the same time, so they don't feel bored or over their heads," said Siu.

According to the new data, in 2021, more than a third (37%) of high school students reported they experienced poor mental health during the COVID-19 pandemic, and 44% reported they persistently felt sad or hopeless during the past year. The new analyses also describe some of the severe challenges youth encountered during the pandemic:

Depending on the professor teaching the class, the diagnostic exam may still be given after three weeks to help students with their decision. In 1994, 89 students took the diagnostic exam: students scoring more than 50% on the quiz could enroll in Schmid's Math 55 (15 students), students scoring between 10 and 50% could enroll in Benedict Gross's Math 25: Theoretical Linear Algebra and Real Analysis (55 students), and students scoring less than 10% were advised to enroll in a course such as Math 21: Multivariable Calculus (19 students).[7]

In 1970, Math 55 covered almost four years worth of department coursework in two semesters, and subsequently, it drew only the most diligent of undergraduates. Of the 75 students who enrolled in the 1970 offering, by course end, only 20 remained due to the advanced nature of the material and time-constraints under which students were given to work.[11] David Harbater, a mathematics professor at the University of Pennsylvania and student of the 1974 Math 55 section at Harvard, recalled of his experience, "Seventy [students] started it, 20 finished it, and only 10 understood it." Scott D. Kominers, familiar with the stated attrition rates for the course, decided to keep an informal log of his journey through the 2009 section: "...we had 51 students the first day, 31 students the second day, 24 for the next four days, 23 for two more weeks, and then 21 for the rest of the first semester after the fifth Monday" (the beginning of the fifth week being the drop deadline for students to decide whether to remain in Math 55 or transfer to Math 25).[3]

Through 2006, the instructor had broad latitude in choosing the content of the course.[12] Though Math 55 bore the official title "Honors Advanced Calculus and Linear Algebra," advanced topics in complex analysis, point-set topology, group theory, and differential geometry could be covered in depth at the discretion of the instructor, in addition to single and multivariable real analysis as well as abstract linear algebra. In 1970, for example, students studied the differential geometry of Banach manifolds in the second semester of Math 55.[11] In contrast, Math 25 was more narrowly focused, usually covering real analysis, together with the relevant theory of metric spaces and (multi)linear maps. These topics typically culminated in the proof of the generalized Stokes theorem, though, time permitting, other relevant topics (e.g. category theory, de Rham cohomology) might also be covered.[13] Although both courses presented calculus from a rigorous point of view and emphasized theory and proof writing, Math 55 was generally faster paced, more abstract, and demanded a higher level of mathematical sophistication. In short, the course gave a survey of the entire undergraduate curriculum of mathematics in just two semesters and might even include graduate-level topics.[3]

Loomis and Sternberg's textbook Advanced Calculus,[14] an abstract treatment of calculus in the setting of normed vector spaces and on differentiable manifolds, was tailored to the authors' Math 55 syllabus and served for many years as an assigned text. Instructors for Math 55[15] and Math 25[13] have also selected Rudin's Principles of Mathematical Analysis,[16] Spivak's Calculus on Manifolds,[17] Axler's Linear Algebra Done Right,[18] Halmos's Finite-Dimensional Vector Spaces[19] and Artin's Algebra[20] as textbooks or references.

From 2007 onwards, the scope of the course (along with that of Math 25) was changed to more strictly cover the contents of four semester-long courses in two semesters: Math 25a (linear algebra and real analysis) and Math 122 (group theory and vector spaces) in Math 55a; and Math 25b (real analysis) and Math 113 (complex analysis) in Math 55b. The name was also changed to "Honors Abstract Algebra" (Math 55a) and "Honors Real and Complex Analysis" (Math 55b). Fluency in formulating and writing mathematical proofs is listed as a course prerequisite for Math 55, while such experience is considered "helpful" but not required for Math 25.[4] In practice, students of Math 55 have usually had extensive experience in proof writing and abstract mathematics, with many being the past winners of prestigious national or international mathematical Olympiads (such as USAMO or IMO). Typical students of Math 25 have also had previous exposure to proof writing through mathematical contests or university-level mathematics courses.

Now that we know that we know the important role nonverbal signals play in communication, how can we use body language and tone to communicate more effectively? Perhaps more importantly, how can we prevent nonverbal forms of communication from falsely influencing our perceptions of others?

It is crucial to provide a variety of books to appeal to different interests, backgrounds, and levels. Try filling your classroom library with some of the titles below and watch as students devour them.

Krosoczka's graphic novel memoir about dealing with his mother's addiction, searching for his father, and growing up with his grandparents is a story that will teach middle school readers that it's ok to struggle and to wish things were different, but that joy can be found even in extreme hardship. For students dealing with parents who struggle with addiction, this book offers hope and the promise that someone else understands.

Zoey has a lot on her plate- younger siblings, helping her friend Fuschia and avoiding the rich kids that surround her. But when a teacher convinces her to join the debate, she learns to see those situations and more in a different way. Will she speak up for herself and those she loves, even if it means risking something she loves?

Fans of Marvel will know Squirrel girl from the comic books, but this prequel novel is designed for younger readers. Students will love the connections between this origin story and the Marvel universe as they find out how Doreen learns to use her powers while still being herself.

Tris has a secret- she's divergent, meaning she could join several different factions in her community. But there's a deeper meaning...a more dangerous meaning to her if anyone finds out the truth. This begins a trilogy that would provide great discussion for 7th grade book clubs or literacy circles.

Undefeated is the incredible true story about "the team that invented football." A true underdog story, the book covers themes of racism, determination, and teamwork. Jim Thorpe's story will inspire and motivate middle schoolers to keep going, even against seemingly insurmountable odds.

Engle's memoir about growing up in California as a girl from Cuba during the Cold War showcases the life of a girl caught between two worlds, both of which she loves deeply. Told in verse, the book takes readers into her life as she shares what life was really like then.