Astronomy Books
My Astronomy Book Suggestions for Intermediate Level
by
Gary Agranat (c)
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This page was last revised July 5, 2007.
Key:
= Books with this symbol
are on a more advanced level.
Some picture icons are freely used to help suggest certain topics.
- The Universe and Beyond
by Terence Dickinson. © 1999. Firefly Books.
-
This book is an excellent introduction to what we know about the universe. It begins
on an Earth-bound scale we can all relate to. It then step by step expands the scale to
the solar system, to nearby stars, to the processes of the galaxy, to nearby galaxies, to
the rest of the universe, and to cosmology.
The particular sciences useful at each scale are nicely discussed.
A more subtle point is that at each scale we are studying the chemistry and physics of higher and
higher energy levels. The book ends with a discussion about extraterrestrial life and
space art. The book is
well illustrated and well written. Suitable for an interested teen. But there are topics
here you won't see in any high school course.
- Cosmic Horizons, Astronomy at the Cutting Edge
edited by
Steven Soter and
Neil deGrasse Tyson. © 2001. AMNH Book.
- A series of chapters on contemporary questions in astronomy.
- The Astronomers
by Donald Goldsmith. NY: St. Martin's Press.
© 1991, Community Television of Southern California.
- This is the companion book to the PBS TV series. The book's quality is
more consistent and better than that of the TV series. More significantly, the book presents
an extensive survey of professional astronomy work and the scientists who carry out that work.
The book therefore provides an interesting bridge from basic understanding to how the science is
actually done. Many illustrations and a narrative style make this book inviting to the general
reader. At the same time, the book brings you to the deep questions of the field.
-
100 Billion Suns--The Birth, Life, and Death of the Stars
by Rudolph Kippenhahn. 1993.
Princeton Univ. Press.
-
This book is the best introduction to astrophysics for the general reader that I have seen.
It is written by one of the pioneers in astrophysics computer modeling. It is well written
as a naturally flowing narrative and detective story.
At the beginning of the book, Rudolph Kippenhahn introduces you to some interesting questions
that come from observing stars. The questions can more easily be seen by arranging the
observational data on the H-R diagram (or color-magnitude diagram).
Computer models running with relatively simple assumptions
turn out to predict many of the features we see.
The early chapters discuss what the simple computer models are like. They trace
how given particular starting masses and compositions, stars evolve with time.
In general, stars find stable
balances between their energy release from nuclear fusion and the weight of their material
gravitationally attracted inward. But stars of low mass and high mass are found to evolve
in significantly different ways. The evolution of high mass stars turns out to be very complex,
and computer models to this day still have trouble predicting just what can happen at the end of
the stars's lives. The end of
the book, therefore, is about what the observational evidence suggests, especially from recent
high energy telescopes on satellites.
Rudolph Kippenhahn was the director of the Max Planck Institute for Astronomie until
he required surgery for a brain tumor. After his surgery he decided he could no longer
devote the same energy to his professional work. He chose instead to resign
and devote his efforts to public astronomy education. This book developed
from a series of public talks. In my judgement, the public has received a rare gift.
- Stars & Clusters
by
Cecelia Payne-Geposchkin. 1979. Harvard University Press.
-
This book makes an excellent follow on to Rudolph Kippenhahn's 100 Billion Suns above.
They both discuss essentially the same subject, what do we notice about stars and how
have we come to understand what we see.
But they each write from a slightly different perspective. Rudolph Kippenhahn wrote from
his experience developing computer models to match observation. Cecelia Payne-Geposchkin
instead wrote emphasizing the observational data.
Her book takes you systematically through
the observational experience: first what can we learn by looking at individual stars?
Each star has intrinsic physical characteristics (color, brightness, and spectral features).
With nearby stars, we can also measure parallax and intrinsic motion, although such measurements
may take years. The parallax gives us distance. And the apparent motion shows us that some stars
have similar motions and therefore they are likely associated with each other.
Those are the stars which form clusters and the more loose associations.
Each star cluster turns out to be a snapshot in time.
It is reasonable to suppose that stars in the same cluster were born at about the same time
from the same starting composition. But stars within a cluster are not all the same. The
major cause for the differences turns out to come from the different starting masses. The
more massive stars tend to burn more brightly and evolve more quickly. A star cluster is a
snapshot in time of many stars of different masses. When we study different clusters, we
get snapshots of different times and different starting compositions. Studying the stars
of the nearby clusters gives us benchmarks for studying the more distant clusters.
The observations are correlated with the computer models which Rudolph Kippenhahn discusses.
Much of our astrophysics understanding comes from the observations of clusters. This is why
most of the rest of Cecelia Payne-Geposchkin's book is devoted to clusters. She carefully
shows how the data from star clusters reveal so much of what we know about the stars and
stellar evolution. The two perspectives of each of these
books, observational and theoretical, nicely complement each other.
- The Milky Way
By Bart & Priscilla Bok.
1984. Harvard University Press.
- This is an exceptional book, written by a highly regarded astronomer and his
wife. They passionately convey the science behind our ever-evolving understanding of
our Milky Way galaxy. Although the last edition came out in 1984, the book covers the field so
extensively that it is still worth the read.
The opening chapter is like a reconaissance, with high quality photos and
detailed descriptions of features that can be seen with the naked eye. Then comes a careful
discussion about the instruments astronomers use and just what is measured. With a
"map" and an understanding of the nature of the data, they then take you on a
journey of what was known at the time of their last edition. They cover similar stellar
astrophysics topics as in Cecelia Payne-Geposchkin's book above. But they take a little
more care in discussing the nature of the research. They cover what we have learned about
the nearby stars, and how those stars are a benchmark for probing more distant stars and
clusters. They discuss the H-R diagrams of the various clusters. They discuss the clouds
and nebulae. And they discuss how we have been able to derive the motion and structure of our
galaxy, often by indirect means -- because we are inside the Milky Way and can only visibly
see part of it. This book fills an important gap between what you can learn from general
level books and how professionals actually come up with what they know.
- Stars
by
James B. Kaler. © 1992.
Scientific American Library.
- Star Factories, The Birth of Stars and Planets
by Ray Jayawardhana. Harvard-Smithsonian Center for Astrophysics.
Turnstone Publishing Group [Harcourt]
-
A well-written book on a junior high school level.
- Variable Stars
by J.S. Glasby. © 1968, London: Constable & Co.
- This book is dated. That is, the astrophysics understanding behind what
is discussed here has progressed since the book was written. Nonetheless, I mention this book
because it gives a systematic, detailed discussion of the many kinds of
variable stars one can observe. The value of this kind of book is that you get the synthesis
of extensive observing experience. There is extensive discussion of the observable features and
how astrophysics was used to try to explain them. The author was at the time the Director of the
Variable Star Section of the British Astronomical Society. The book was written both
for amateurs and professionals. You might still be able to find used copies if you search
around.
- Light at the Edge of the Universe
by Michael D. Lemonick.
1993. Princeton Univ. Press.
- This book is an interesting view of the state of cosmology after the
COBE microwave background results came out in the early 1990's.
The author is a former scientist turned
science journalist. He sought to understand the current state of cosmology for himself.
He devoted a couple of years to interviewing and following a number of key scientists in the field;
he followed the leads of the questions on their minds as well as questions of his own.
He often let the scientists and the results speak for themselves.
Therefore, you get to see the differences in ideas, personalities, backgrounds, approaches
to the work. You get an impression of how those differences contribute an important part to the
science. Like an assistant detective, it is if you are able to tag along with Mr. Lemonick;
and your are confronted with the same puzzle that he was confronted with. The working picture
that develops in your mind is one, not of answers, but of continually evolving questions that
the answers create.
-
The First Three Minutes
by Steven Weinberg.
1977, 1988. Basic Books.
- The Inflationary Universe, The Quest for New Theories of Cosmic Origins
By Alan H. Guth.
Forward by Alan Lightman. Addison-Wesley. © 1997.
- Dr. Guth's own account of how he came up with Inflation Theory.
The book is very insightful and remarkably straight forward.
- Also see the physics book suggestions below.
- A History of Astronomy
by Anton Pannekoek. 1961.
Dover.
- The Exact Sciences in Antiquity
by O. Neugebauer. 1969. Dover.
- The Cambridge Illustrated History of Astronomy
edited by Michael Hoskin. 1997. Cambridge University Press.
- Astronomies and Cultures in Early Medieval Europe
by Stephen C. McCluskey. © 2000.
Cambridge University Press
(Publisher's link gives more details).
- Johannes Kepler and the New Astronomy
by James R. Voelkel.
© 1999. Oxford University Press.
- A thoughtful book written on a high school level.
- Isaac Newton by James Gleick. © 2003.
Pantheon (Random House). ISBN 0-375-42233-1.
- Also see the related science books, especially books about
physics and math.
- My
History Pages.
-
Getting the Measure of the Stars
by Cooper & Walker. 1989.
Adam Hilger.
-
Experiments in Astronomy for Amateurs
by Richard Knox.
1976. St. Martins's Press.
-
Projects help you measure basic celestial motions, that is, the motion of the Earth with
respect to the Sun and Moon. You can build several kinds of sundials, including one that
measures altitude angle instead of azimuth. If you have learned some celestial navigation,
you may notice that you essentially use the same mathematical relationships; but the
variables are different. The last project is a circular slide rule to predict the position of
Moon.
- [ See my note about this book on
my Astrolabe Page.]
Astrophysics by Wavelength
- The Discoveries: Great Breakthroughs in 20th-Century Science, Including the Original Papers
by Alan Lightman. Pantheon. 2005.
- Alan Lightman
- Great Ideas in Physics:
The Conservation of Energy,
The Second Law of Thermodynamics, The Theory of Special Relativity, and
Quantum Mechanics.
© 2000. McGraw Hill.
This is an excellent book for students beginning college physics. The first
half of the book especially is a good step-by-step examination
from the point of view of energy. The math is
on a high school level. Yet the discussion takes you deeply into the ideas of
college level courses -- and is clearer than what I have often
seen in college!
- A Sense of the Mysterious, Science and the Human Spirit
© 2005. NY: Pantheon Books.
A reflection on physics and humanities, after Professor Lightman shifted
his professional work from physics to writing.
-
The Extension of Man--The History of Physics before the Modern Age
by J.D. Bernal. 1972. MIT Press.
- An intuitive look at how physics developed from prehistory to
the beginning of the 20th century. [
excerpt ]
- Emilio Segrè
These books are light but informative historical narratives.
The last one is a biography of the Italian-American physicist Enrico Fermi.
- The Story of Physics
by Lloyd Motz and Jefferson Hane Weaver. © 1989, 1992. NY: Avon Books.
- I am very hesitant to suggest this book. However, I think it can be
valuable, and so I will include it here. The book has several strengths. In my mind, the
most important strength is that the book presents a continuity of thinking in how physics
developed from the time of the ancient Greeks to the twentieth century. The perspective
comes from a working physicist at a university. It is written on a level such that it is
absolutely relevant and usable to any undergraduate who is studying physics. The book is
an accomplishment and it fills an important niche. No one physics course can give you
what is presented here. Often, courses don't even try.
However, that stength also has within it a weakness. The book seems to be so heavily a
college perspective; it is as if you can explain the world without ever leaving campus.
Some of the biographical discussions don't seem any deeper than what one can get in an
encyclopedia.
In my judgement, the actual history was probably much more complex
than what is portrayed here. Consider for example the writings of the NYU mathematician
Morris Kline, or Ian Stewart's
Letters to a Young Mathematician (below). This book does give you valuable insights
into how scientists and mathematicians in the past may have thought; and it shows a
remarkable continuity in how individuals built on the work of their predecessors and peers.
Professor Motz apparently had given much careful thought to how the whole physics story
developed. However, at some point you may feel the need to dig more deeply. If you yourself
never think about physics off the campus, you might not realize there is something missing.
I have essentially similar comments for a similar book written by this pair,
The Story of Math (below).
That book similarly presents a very useful and intersting
continuity of thought that underlies the history of Western math. Such a perspective
would be valuable to any college student who wants to put together the background better.
The background presented in The Story of Math is especially relevant to physics students.
But again,
at some point you may realize you need more than what you can get in this kind of book.
The pair also wrote the book, The Story of Astronomy. I have not read that, and so
I can't offer any comments on it.
I think the value of these books come especially from being able to see the whole continuity
of how the fields developed, based on how the actual questions and results kept leading to
new experiences. There is background given here that I wish I had seen during my college
courses. For example, I had never understood where the vector algebras had come from. They
were acutally the product of some deep physics questions of the 19th century. Instead, I
had to learn them as a matter of mechanical technique. One strong impression I came away with
after reading The Story of Physics is that modern physics developed out of two
significantly different kinds of experiences. One kind came from sharply noticing what is in
the world, and from then trying to characterize it and explain it. But the other kind came
from applying mathematical arguments to physics to extrapolate what would logically come.
The two kinds of experiences are not necessarily the same. See my comments below with
Morris Kline's book, Mathematics, the Loss of Certainty.
Lloyd Motz has been a physics professor at Columbia University
for many years. His co-author, Jefferson Hane Weaver, received a PhD. at Columbia,
but apparently not in physics.
-
Discovering the Natural Laws -- The Experimental Basis of Physics
by Milton A. Rothman. © 1972, 1989. Dover.
- Six Roads from Newton - Great Discoveries in Physics
by Edward Speyer. © 1994. Wiley.
- George Gamow
- Thirty Years that Shook Physics, The Story of Quantum Theory
Originally published: Doubleday, 1966. Dover edition 1985.
-
A personal, insightful account by Gamow, who had been a student of Niels Bohr.
- Biography of Physics.
1961. NY: Harper and Brothers.
- Brian Greene.
-
The End of Physics -- The Myth of a Unified Theory
by David Lindley. 1993.
Basic Books.
-
The title of this book seems to come from a lecture by Stephen Hawkings in 1979,
"Is the End of Theoretical Physics in Sight?" Lindley's theme seems to be an appeal
for physicists to not forget about the need for experimental proof for a theory.
The notion apparently is that if Supergravity and Superstring theories are accepted without
proof, perhaps that would be a different sort of "end" to physics.
(This is not the same sort of book as The End of Science, by Horgan).
- Lee Smolin
- Three Roads to Quantum Gravity
© 2001. Basic Books.
- The Trouble With Physics: The Rise of String Theory, The Fall of a Science,
and What Comes Next
© 2006. Houghton Mifflin.
-
The Particle Garden
by Gordon Kane. 1995. Addison Wesley.
-
Chaos
by James Gleick. 1987, 1988.
Viking Penguin Books.
- Richard Feynman
Probably anything you can read by Feynman will be
thought provoking and interesting.
- The Character of Physical Law. © 1967. MIT Press.
(BBC 1965).
- QED - The Strange Theory of Matter and Light. © 1985.
Princeton University Press.
- A Different Universe, Reinventing Physics from the Bottom Down
by Robert B. Laughlin. 2005. Basic Books.
- The Science of Radio
by Paul J. Nahin. 1996. American Institute of Physics Press.
- The Path of No Resistance, The Story of the Revolution in Superconductivity
by Bruce Schechter. © 1989. NY:Simon & Schuster.
- An intelligently written account of how high temperature supreconductivity
developed and then suddenly was thrust into the spotlight during the late 1980's.
An interesting taste of another part of the physics community (solid state physics).
- Atmosphere, Climate, and Change
by
Thomas E. Graedel and Paul J. Crutzen.
1995. Scientific American Library, HPHLP.
- This book introduces to the interested general reader the science of
climate modeling. The authors particularly give attention to atmospheric chemistry
(Paul Crutzen's strength).
But they discuss the many complex interacting factors: e.g., life processes, air and
ocean circulation, man made contributions, etc. They show you how climate models are
made and used. They give details about how
the one, two, and three dimensional grid systems are set up and used. And you get to see
their strengths and weaknesses. Using the climate models and the past evidence recorded
in the rocks and ice, the authors discuss what can be said about what happened in the past.
And they project what can be said about the future.
The end of the book discusses a long term Earth climate prediction of about a billion
years into the future. The prediction is that the gradually warming sun will
significantly alter the Earth air-water-land chemistry cycles to the point that the Earth will
then no longer be able to support life. (This is much sooner than the time 4 ½ billion
years from now when astronomers have claimed life will end; their prediction was based
on the time they expect the Sun to change to a red giant.)
-
Ice Ages -- Solving the Mystery
by John Imbrie and Katherine Palmer Imbrie.
© 1979. Enslow Publishers.
- Takes you through the evidence, and how the scientific ideas
actually came about and developed.
- Forecast Earth, The Story of a Climate Scientist, Inez Fung
by Renee Skelton. © 2005. Scholastic.
- This is a book in the "Women's Adventures in Science Series",
written for about a junior high school level.
Most of these books address how life on Earth could have begun.
- Peter Ward and Don Brownlee
(Univ. of Washington).
- Rare Earth, Why Complex Life is Uncommon in the Universe -
A book on astrobiology and Earth history
By Peter Ward and Don Brownlee. Copernicus Books © 2000.
- This book presents a two part hypothesis, that microbiology may be common in the Universe,
but higher life forms like animals may be rare. These ideas derive from a synthesis and
extrapolation of current work on astrobiology. In recent years that work has been more critically
examining what enables an astronomical "habitable zone" to exist around a star,
and what caused the past mass extinctions on Earth. The authors have thought deeply about
the state of current work. In this book they present their conclusions about what that
work logically implies. The conclusions are not obvious; but there is a careful analysis
behind them, and the consequences are profound.
In other words, the book poses a question that you have to think about.
The authors are a geologist-paleontologist and an astronomer who now work in astrobiology at the
University of Washington.
- Rare Earth Book Website
- The Life and Death of Planet Earth By Peter Ward and Donald Brownlee.
© 2002. Times Books, Henry Holt and Company.
- This book is presented along similar lines as the one above.
The focus in this case is on how the physical conditions on Earth may
evolve so that life can no longer
survive. The authors came to conclude that there are a series of stages, not just one event.
The determining factors for life's survival are found to be Earth's surface temperature and
the carbon dioxide concentration in the atmosphere. These are driven by
the gradual brightening of the Sun and the balance of chemical
processes on Earth between the atmosphere, oceans and rocks.
- Also see Atmospheric Science & Climate books above.
- Also see
Ends of the World: Astrobiology and Armageddon
An online video talk by the authors on July 8, 2002.
-
Cradle of Life -- The Discovery of Earth's Earliest Fossils
by
J. William Schopf. © 1999. Princeton University Press.
-
The Emergence of Life
by Sidney Fox. 1988. Basic Books.
-
The Origins of Life
by Cyril Ponnamperuma. 1972. E.P. Dutton.
- Marston Bates
- Life Pulse, Episodes from the Story of the Fossil Record
by Niles Eldrege (AMNH). © 1987. NY: Facts On File.
-
Exobiolgy Page
- A Long Way From Euclid
by Constance Reid. 1963. Crowell.
- A History of Pi
by Peter Beckmann. 1971.
Golden Press. Barnes & Noble Books edition 1993.
- A passionate, thought-provoking
narrative, written on a junior high school level.
- The Historical Roots of Elementary Mathematics
by Lucas N.H. Bunt,
Phillip S. Jones, and Jack D. Bedient. © 1976 and © 1988.
Dover.
- Euclid's Window - The Story of Geometry from Parallel Lines to Hyperspace
by Leonard Mlodinow. © 2001. The Free Press (Simon & Schuster).
- The Mathematical Career of Pierre De Fermat, 1601-1665
by
Michael Sean Mahoney.
1973, 1994. Princeton University Press.
- The History of the Calculus and its Conceptual Development
by Carl B. Boyer. 1949. Reprinted by Dover, 1959.
-
This is a well written, relatively short book on the development of calculus.
It is through this book that I finally came to understand on what logical basis calculus is built.
That is, the fundamental concept of calculus is the limit of an infinite sequence of elements.
If one wants to really utilize calculus and understand why it works, sooner or later one needs to
come to terms with precisely what it is.
Learing calculus can be such a challenge because it is not simply a matter of going out into the
world, seeing how the world works, and synthesizing a logical system from that. The development of
calculus required long struggles of intuitive thinking, over many different historical periods
spanning 2500 years. Therefore, one is confronted with having to understand the intuition as well,
and how well that intuition turned out to work.
That doesn't mean that calculus is
too difficult to understand. In order to really understand it, one has to taste the problems
from which mathematicians eventually came up with solutions.
For example, how does one equate the area of a curved figure with that of a polygon? In
ancient Greece, where deductive geometry was first developed, mathematicians
didn't equate them. The shapes were considered too different. Instead, they found that
one could equate the ratios of aspects of various shapes. ("What is the ratio of
the areas of two circles? The same as that of the squares constructed on the diameters of the
circles.")
Archimedes determined that one could find the area of a circle by finding the areas of
circumscribed and inscribed regular polygons with more and more sides (the method of exhaustion).
But he might not have conceived that the two kinds of shapes are equivalent. Therefore, the notion
that a regular polygon can be equated to a curved figure by the limit of an infinite sequence
might not have been the kind of problem that would occur to him. He solved a geometry problem
of areas, not a problem of infinite sequences.
Often when math textbooks mention the work of past mathematicians, the problems are framed
only in modern terms. Often, you don't see what the original problem was, and you miss
something important. You can miss what the original intuition was about, what it solved that
wasn't solved before.
You can also miss the problems that the new intuitions created.
Some of those intuitive solutions, such as
infinitesimals, which even Newton and Leibnitz invoked, turned out to be dead ends.
And yet, infinitesimals are still taught in our textbooks now!
Calculus originated from trying to intuitively understand
and work with real problems we can grasp in the real world. However, the solution of
those problems eventually led calculus to be defined more abstractly in terms of number theory.
One condition naturally led to the other. If one wants to have an intuitive sense of calculus,
one needs to naturally also work through the process, in order to see what the modern notion is,
and why it is valuable the way it is.
What I especially like about this book is that you get to see what the mathematicians of the
past were struggling with and how far they were able to go. Often in math classes and in math
books, I only have seen the end results of what mathematicians did. I have to learn their
theorems, I have to learn their techniques. And often it is as if they have been put on pedastals,
somewhat removed from the human turmoil I have to work through in order to figure out just what
they did. This kind of book evens the playing field and shows that mathematicians are quite
human. I believe that it is through such insight that one can then really understands what they
did and what they weren't able to do.
For example, this book's chapter on Newton and Leibniz is remarkably
short, only 36 pages out of a text of about 310 pages. One can more manageably see just what they
did in the context of the long struggles which preceeded them and the struggles of the following two
centuries.
In order for calculus to be made logically consistent, number theory had to be made logically
consistent. The final stories of the book explain how number theory came to take its modern
form as well.
The next book,
Understanding Infinity, The Mathematics of Infinite Processes, by A. Gardiner,
is a good follow-up book.
-
Understanding Infinity, The Mathematics of Infinite Processes
by A. Gardiner.
Dover © 2002; updated from a Springer-Verlag 1982 edition.
- Morris Kline
- Mathematics in Western Culture.
1953. Oxford University Press.
- Mathematics and the Physical World.
1959. Dover edition, 1981.
- Mathematics for the Nonmathematician.
1967. Dover.
- Mathematical Thought from Ancient to Modern Times
3 volumes in paperback. Oxford University Press. 1972.
- Mathematics, the Loss of Certainty.
© 1982. Oxford University Press.
- Of the books by Kline I list, this is the most profound. I needed
several years to learn how to read this book. The effort was worth it. In this book
Kline probes how mathematical knowledge is not necessarily physical knowledge about the
real world.
The discovery of that fact seemed to come as quite a shock to many professionals.
(The discovery may still come as shock to many people as they mature even now.)
The realization in the 19th and 20th centuries provoked the development of the different
major schools of mathematical philosophical thinking. The battles they so vigorously
fought turned out to be unwinnable.
The way mathematics is taught in schools generally shields you from discovering such a
realization. In high school geometry, for example, you usually begin with the definitions
and axioms. But if you carefully examine how mathematicians actually use the math,
the definitions and axioms were created in order to be consistent with mathematical experience;
they were not the starting point. I don't mean to downplay the value of logic. Nor do I
mean to diminish the fact that applying the logical aspects of math to the real world is
so vitally important to our modern civilization. But if you care enough, sooner or later
you discover that mathematical logic doesn't necessarily tell you that you are solving a
problem in the real world.
This is not just a problem for mathematicians. Problems turn up all the time in the
practical world. As an example, when the Columbia space shuttle was damaged on launch by
insulation debris, a group of inexperienced engineers were given the task to analyze the
damage through a computer model. Unfortunately, the model used, called Crater,
was designed to analyze damage only on a smaller scale. The engineers mistakenly extrapolated
the numbers they got from their computer runs to the larger scale. It didn't seem to occur
to them that they made a bad assumption. They passed on their conclusion that the launch
damage would not create a structural problem for the shuttle wing. They made a big mistake!
The Columbia burned up on re-entry, due to structural failure.
Although all mathematical experience begins in the real world of our own
experience, the strength of math is that it tries to be consistent with itself.
As mathematicians more and more came to focus on this consistency, they discovered how
their mathematical arguments could contain subtle assumptions. They then tried to
recognize the assumptions in their arguments and create a more general framework for math.
In consequence they created mathematical systems which were much more abstract. But many
of those systems turned out to be useful for physics: e.g., non-Euclidean geometries,
vector and tensor algebras, infinity and the infinitesimal, etc. It can be argued that
one of the major thrusts of modern physics is to utilize these more abstract mathematics
to discover new physics. As a consequence, one can see why some physicists take great
pains to warn their students to not get blinded by just following formalisms. It is
relatively easy to apply formulas. It takes more mature thinking to take care of
hidden assumptions.
- Mathematics and the Search for Knowledge.
© 1985. Oxford University Press.
- Ian Stewart.
- Letters to a Young Mathematician (Art of Mentoring)
© 2006. Perseus Books Group.
- Why Beauty is Truth, A History of Symmetry
© 2007. Basic Books.
This is a nicely written book on the general level. I don't necessarily agree that "beauty
is truth", but I do like the book. The underlying theme is algebra. But related
areas, like geometry and physics are interwoven into the stories.
Each chapter focuses on a particular
mathematician and a particular relevant topic associated with that person and time. As you go
along your wisdom develops as well as your knowlege. The book nicely complements John
Derbyshire's Unknown Quantity below.
The subject of this book is also related to Mario Livio's The Equation That Couldn't Be
Solved, How Mathematical Genius Discovered the Language of Symmetry; I haven't yet, however,
fully read Mario Livio's book, and so I'm not ready to comment on that. Of these three books,
in my judgement, Ian Stewart's book is the most accessible for the curious beginner. In my case,
my graduate engineering education encompassed lots of of advanced calculus. However, I was never
really exposed to the underlying ideas that unify algebra and motivate the work. I felt I missed
something important. I find these kinds of books help give me much more insight.
-
Unknown Quantity, A Real and Imaginary History of Algebra
by John Derbyshire. © 2006. Josesph Henry Press (National Academy of Sciences).
- My Brain is Open, The Mathematical Journeys of Paul Erdös
by Bruce Schechter. © 1998. Simon & Schuster.
- A biography of the Hungarian born mathematician Paul Erdös.
"We mathematicians area all a bit crazy," the German number theorist Edmund
Landau told Erdös when they met at Cambridge University in 1935. It was an
observation with which Erdös, young as he was, could not but agree, though he found
it more amusing than troubling. Crazy or sane made little difference to Erdös; from
the beginning of his mathematical journeys he went to great lengths to meet anyone who
could produce beautiful proofs and conjectures, and he was very difficult to put off.
[From the beginning of Chapter 4.]
To say that he was eccentric is probably an understatement. But does that matter?
Paul Erdös was apparently a very prolific mathematician. His life and his math
make an interesting story. Part of what I like about this book is that one gets a taste of
Paul Erdös's childhood. Although his parents seemed to have been over-protective,
the environment in and out of his house in Hungary seems to have been very stimulating.
John von Neumann, Leo Szilard, and Edward Teller were among some of the other remarkable
scientists who grew up in Hungary at that time. What I also like about this book is that
it is very readable. An interested teen could follow both the math and the life story.
The author got his Ph.D. in physics at M.I.T. He also wrote The Path of No Resistance,
an intelligent account of how high temperature superconductors suddenly came on the scene in
the late 1980's. I recommend that book as well.
- Mathematics and the Imagination
by Edward Kasner
and James Newman. © 1940, renewed 1967. Simon and Schuster.
- The Story of Math
by Lloyd Motz and Jefferson Hane Weaver. © 1993. NY:Avon.
-
See my comments above for The Story of Physics.
As with its sister book, The Story of Physics, I am extremely hesitant to suggest
The Story of Math. In my mind, this way of viewing math is like looking
through a peculiar narrow filter; the filter seems to resemble a view that has never left
the college campus. For me, who feels creative with math and about where math comes from,
this view looks distorted. I am willing to mention the book because for some people, and
for me at certain moments, this book can be useful. Its strength is that it gives you
a remarkably extensive continuity of thought of Western math. It gives you a background
of why the math you are taught as an undergraduate is there. At a certain stage of
undergraduate learning, a student in say physics, engineering, or any applied science which
utilizes the math may find this book useful. This book can fill in details which you might
not otherwise get, and which can make the reasons behind what you do much clearer. But this
book is so conceptual in its outlook that it systematically bypasses what the creativity may
really be like. Furthermore, like is sister book, the biographies tend to be encyclopedic.
The explanations tend to be excessively wordy. And the way the explanations are written
require the reader to know more than the authors seem willing to admit. Before you read this
book, I recommend instead Ian Stewart's
Letters to a Young Mathematician (Art of Mentoring) (see above).
Math and Learning
- Mind Over Math
by Dr. Stanley Kogelman and Dr. Joseph Warren. © 1978. NY:McGraw Hill.
- This is a self-help book to help you if you feel anxiety about math.
It is especially useful if you feel your math schooling in the past was
traumatic. I think this is an excellent book.
- Making Sense, Teaching and Learning Mathematics with Understanding
by James Hiebert, Thomas Carpenter, Elizabeth Fennema, Karen C. Fuson, Diana Wearne,
Hanlie Murray, Alwyn Olivier, Piet Human. © 1997 University of Wisconsin. Heinemann.
-
Of the books I have seen on math education for grade school level, I especially like this one.
It makes immense sense to me. And my experiences seem in agreement with the theses
put forward in this book.
- Learning and Teaching Elementary Mathematics -- Teachers' Understanding of Fundamental
Mathematics in China and the U.S.
by Liping Ma. © 1999. Lawrence Erlbaum Associates.
-
This is a thought-provoking book. Liping Ma came to math education in an unconventional way.
She grew up in China during the Cultural Revolution. At that time millions of city children
were sent to distant rural villages and nomad homelands to be "re-educated". They
were to work in the fields as peasants or tend animals on the range. [Many of those
children afterwards considered those years "lost years" of their education.
Many struggled afterwards to try to catch up.]
When Liping Ma finished eigth grade she was sent to a rural village in southeast China, and
she worked in the fields. After a few months the village elders asked her to instead teach
their children math at the school. She was the most educated person in the village.
And so she taught, and she learned from her experiences. She didn't learn pedagogy.
She learned by what made sense to her. In time she became the education
supervisor for the entire county. Later she became a Ph.D. student in the U.S. This book is
her thesis. When she came to this country, she was astonished by problems in classrooms
which she knew would be problems and yet were not in the language of math education here.
She has some very interesting things to say. Her main point is that she thinks need to be
able to teach a profound understanding and be able to develop that for themselves. She
points out that Chinese school math teachers generally do not finish college; while
many American math teachers are required to get masters degrees. And yet Chinese students
and teachers typically score better in comparison tests. And so she is claiming,
a facillity with higher math isn't necessarily what is needed; teachers need to be able to
professionally teach well, and understand what they are doing. Most of her thesis is a
comparison study she conducted. With it she tries to illuminate some underlying issues.
From what I've read of reviews in math
education newsletters, I suspect a number of math educators aren't able to understand
underlying aspects. [In my judgement, there is a deeper psychological aspect than what
this thesis can address. Nonetheless, the thesis raises what I think are valid points. It
should raise questions.]
-
Book Review- Knowing and Teaching Mathematics by Roger Howe. AMS.
-
The publisher's page about the book
-
A related short essay by by Angela Andrews at the
National Council of Teachers of Mathematics web site.
- On Writing Well
by William Zinsser.
1998 (6th edition; there are probably later editions by now).
Harper Perennial (Harper Collins).
After I read this book, I realized that many books on non-fiction and
technical writing are written
too conceptually. This book invites you into the experience in a very practical way.
- Bird by Bird, Some Instructions on Writing and Life
by Anne Lamott. 1994. Anchor Books.
For creative writing.
- Some links to help with writing.
In my website about the early history of space flight, I listed many books I used for
my research. About several dozen of those books are NASA histories which are available
online through the NASA history website. See the
References Page at
The Early Space Age in Stamps -- An introduction to the early history of space flight.
Astronomy Intermediate Book Suggestions/ Created May 17, 1997, last revised July 5, 2007,
updated December 02, 2007.
My reviews are copyrighted.
Mail to me
Interview with James Gleick about his biography of Newton
, by Leonard Lopate on WNYC in NY, September 1, 2003.
