28 NOVEMBER 2007	Surviving Math Exams
6:30-7:30pm	[short presentation] Strategies for studying math and preparing for final exams.
McMaster University, MDCL 1102

26 NOVEMBER 2007	Newton's Mind - Interdisciplinary Learning Object
10am-2pm	[Ontario Mathermatics Education Forum] ... Learning object, created at McMaster University, for students to discover and explore the complex mind of Isaac Newton. Web site: http://www.ltrc.mcmaster.ca/newton/. Discussion of rationale for construction of the object, and critique of use of online resources.
Fields Institute, 222 College Street, Toronto

PAST PRESENTATIONS (2006)

5 DECEMBER 2006	The Mind of Isaac Newton
tba	[Learning Technology Symposium; with Kathy Garay, Bill Harris and Muriel McKay] Learning object, created for students to discover and explore the complex mind of Isaac Newton. Web site: http://www.ltrc.mcmaster.ca/newton/. Rationale for construction, and critique of use of online resources.
MDCL 3020, McMaster University

30 NOVEMBER 2006	Transition from Secondary to Tertiary Education - A Modern Rite of Passage
11:30am-1:30pm	[CLL workshop] The passage from secondary to tertiary education is, in many ways, critical to students' success, their choice of a program of study and future career. How well students learn concepts, gain thinking skills and adopt learning strategies and then transfer these to their (new) university environment is instrumental for their success in every course that they take. Good high school students are not necessarily good and successful in university. On the other hand, some students who appear to enter university courses with lower learning skills recover quickly and are successful. In this workshop we plan to discuss issues and identify strategies that instructors, teaching assistants, and everyone else involved with first-year students (course coordinators, student advisors, etc.) can use to help our students adjust to McMaster university learning -and other- environments.
McMaster University, T13-105

27 NOVEMBER 2006	Surviving Math Exams
6:30-7:30pm	[short presentation] Strategies for studying math and preparing for final exams.
McMaster University, location to be announced

23 NOVEMBER 2006	My Life as Researcher in Math Education
4:30-5:30pm	[invited talk] Like many of us, I have worked with mathematics in a variety of ways: as researcher in differential geometry and mathematics education, teacher in high school and university, supervisor of undergraduate and graduate students, and as author and editor of mathematics monographs. I have talked about mathematics at various public events, and wrote about geometric ideas in art and architecture. In this lecture, I plan to speak about how these experiences have inspired and guided me through my life as researcher in mathematics education. In particular, I will focus on my research related to the teacher-training course for undergraduate students that I created (for instance, students' understanding of the concept of a function and its graph, and analysis of teaching diaries), development of a theoretical model for the high school to university transition, and analysis of relation between students' high school mathematics knowledge and experience and their success in first-year mathematics courses.
Concordia University, Library Building, 9th floor, room LB-921.04 1455 de Maisonneuve Blvd. West, Montreal, Quebec

21 NOVEMBER 2006	Space and Dimension
9:30-11am	[lecture for high school students] What does the space that surrounds us look like? Can we deternine whether it Is finite or infinite? In this presentation, we will examine several case studies that will help us understand things a bit better. What is the shortest path between two points in space? How would our mundane three-dimensional existence change if we were suddenly pulled into the fourth dimension? How do mathematicians describe black holes? We will develop a reasonable scenario for time travel into the future.
Bishop Tonnos Catholic Secondary School, Ancaster

7, 16, 21 NOVEMBER 2006	Math Problem-Solving
4:30-5:30pm	Preparation for Putnam Mathematics Competition.
BSB/135, McMaster University

21 OCTOBER 2006	Transition From High School to University - Issues and Models
10am-2pm	[Ontario Mathermatics Education Forum] Perspecives on transition, from a variety of angles: high school, college, university, and research in mathematics education
Fields Institute, 222 College Street, Toronto

19 OCTOBER 2006	Expectations, Challenges and Successes in Managing Large Classes
3:30-4:30pm	[invited seminar] We all have concerns about large classes and inadequate teaching resources, but we under-utilize one of our most valuable teaching resources: our own undergraduates. Experience with undergraduate TAs at McMaster (part of which is the course "Teaching mathematics" designed by Dr Lovric) suggests both that undergraduate TAs bring a number of important advantages to the classroom, and that they count their teaching experience as one of the most valuable aspects of their own education. Besides addressing general logistics problems related to teaching large classes and discussing the ways in which we deal with them, I plan to outline the design of the "Teaching Mathematics" course, and to discuss various issues related to both the course and to students' performance as teaching assistants.
York University

19 OCTOBER 2005	Modeling Universe
9:30pm - 10:20pm	[Engineering and Science Olympics] How do mathematicians model our Universe? What are the most important features of their models, and to what extent are they realistic? We will present several concepts - including dimension, curvature and metric - that will help us understand things a bit better. Using the notion of space-time, we will explain how mathematicians think of phenimena such as black holes. Are wormholes matter of science fiction, or can they possibly exist? Can we make time travel work?
McMaster University, BSB 108

6 OCTOBER 2006	Concept of Dimension
9:30am - 10:20am	[Science 2B3 (Big Questions) guest lecture] Concept of a spatial dimension. Developing ways of thinking about fourth, fifth and higher dimensions. Case studies of transition from lower to higher dimensions.
McMaster University, TSH/120

30 JUNE - 5 JULY 2006	Suggestion For A Theoretical Model For Secondary-Tertiary Transition In Mathematics
TBA (will appear in conference program)	[ICTM3 - Third International Conference on Teaching of Mathematics] Abstract: The transition ('gap') between secondary and tertiary education in mathematics is a complex phenomenon covering a vast array of problems and issues. Although there is evidence of similar gaps in other disciplines in science and beyond, it seems that the transition in mathematics is by far the most serious and the most problematic. Based on certain anthropological notions, we suggest a model for the secondary-tertiary transition in mathematics. Although we focus on the area of mathematics, and on transition between a secondary institution and university (and, to a lesser degree, college), the model could be applied, with minor modifications, not only to other transitions in mathematics (primary-middle, primary-secondary, etc.) but to other areas as well. This model provides a useful lens through which we can examine the process of transition from secondary to tertiary mathematics, and also offer ways of improving present strategies and suggest new ones.
Marmara Hotel, Istanbul, Turkey

27 JUNE 2006	Mathematics - Can't Live With It, Can't Live Without It
5:15-6:15pm	[Department of Mathematics Invited Colloquium] What is the place of mathematics in modern society? The range of applications of mathematics has never been as broad as it is today. Paradoxically perhaps, the number of people who are interested, or say they are good at math, or decide to study math has been dwindling ... How important is it to know mathematics? Examination of the role and politics of mathematics and an analysis of issues in teaching and learning mathematics will lead us to fundamental questions, including the one which, quite possibly, cannot be completely resolved: what is mathematics?
Physics building, room 2.52, University of Fribourg, Fribourg, Switzerland

17 MAY 2006	Assessment and Background Knowledge in Mathematics
1-2pm	[Invited Presentation] Online and paper testing, multiple choice, etc. McMaster experience.
Mohawk College, Hamilton

3 MAY 2006	Stories About Infinity
time: 10:30-11:30am	[McMaster Accelerated Students Workshop] Infinity has many faces. Sometimes, we perceive it as a number larger than all numbers. For indigenous people of Australia and New Guinea, infinity begins at six. For the Moors - creators of the most beautiful mosaics the world has ever seen - infinity was in a repetition of a single artistic motif. Infinity is eternity, divinity, love, death ... Modern mathematicians have embraced infinity as one embraces a good friend; but a few have contemplated suicide rather than being forced to face it. Georg Cantor, early explorer of infinity, died in a mental institution. What exactly drove him to insanity? Does infinity really exist? If so, what is it? Where can we find it? Is our universe large enough to encompass infinity?
McMaster University, HH302

29 APRIL 2006	Living With Functions
10am-2pm	[Ontario Mathermatics Education Forum] Students' understanding of a concept of a function and its graph. Issues realted to using functions in various contexts.
Fields Institute, Toronto

27 APRIL 2006	Mathematics and Beauty of Mosaics in Islamic Architecture
Lecture: 10am-10:50am; question-and-answer follows, ends between 11:30-11:45 For information, email Sue Prior sprior@utm.utoronto.ca or call 905-828-5454	[Canadian Perspectives Lecture Series, University of Toronto, Mississauga] There is so much to look at and admire in Alhambra Palace (Granada, Spain) - exquisite rooms, decorated with stone and wood carvings, finest ornaments, and calligraphy; night sky represented in ceilings built of thousands of pieces of wood; gardens, courtyards and fountains; monuments, towers, archways - the list is endless. Quite possibly, an immense wealth of ornamental patterns, friezes, mosaics, star designs, and brickwork motifs tops the list. Among those, mosaics are perhaps the most interesting and the most intriguing. Scientists and artists working in the Islamic world pushed geometry to its limits, creating patterns and configurations whose sophistication has never been surpassed. Investigating numerous possibilities, based on experience and long tradition, builders of mosaics in the Alhambra created them all in the sense of the mathematics theorem on the classification of plane crystallographic groups (or wallpaper patterns). Mosaics are an invitation for a 'dynamic' experience, different from enjoying a picture of a landscape. This presentation suggests the use of a vocabulary from geometry to express some of our visual experiences.
University of Toronto, Mississagua, Kaneff Building (Matthews Auditorium)

11 APRIL 2006	Life is Too Short for Long Division
7:00pm-8:00pm	[Science in the City lecture series] 1, 1, 2, 3, 5, 8, 13, 21 caught you! Were you staring at those numbers trying to make some sense of them? Have you guessed the next number in the sequence? Mathematics is everywhere around us. Whether it's guessing the tax on the purchase we are about to make, calculating our body mass index, reading the sports stats page in a newspaper, figuring out how much paint we should buy to paint the bedrooms or trying to solve that Sudoku puzzle ­ we cannot avoid using numbers. This lecture will suggest ways of thinking about mathematics that we can all embrace and apply in our everyday situations. Although there seems to be just too much math to learn, Professor Lovric will convince you that a few basic concepts will significantly enhance your understanding of a whole variety of problems that are mathematical in nature. The math that we need in our lives is ­ quite often ­ not what we have been taught in school. Professor Lovric will encourage participants to think about math in a new way ­ not as an object of fear and frustration (or bad memories) ­ but as a useful and creative new friend, that will help us make sense of many things. and the answer to that math teaser is 34 each number is the sum of the 2 numbers preceding it!
This is a free public lecture. All are welcome! where: Hamilton Spectator Auditorium, 44 Frid Street, Hamilton when: Doors open at 6:30 p.m. Lecture begins at 7 p.m. To reserve your seat e-mail sciencecity@mcmaster.ca or by phone 905-525-9140, extension 24934

29 MARCH 2006	How Many Mathematicians Does it Take to Change a Lightbulb?
5:00-6:00 pm	[Session for high school students] We work on interesting mathematical problems, mostly related to fun things from counting and number theory.
McMaster University, HH312

16 MARCH 2006	Math of Weather Forecasting
12:30-1:20pm	[Applications of Math in theThematic Thursdays series of lectures] In this lecture we will discuss mathematical models that are used in weather forecasting. Analysis of such models will lead us to the concept of chaotic behaviour. We will try to understand why is it not possible to calculate accurately a weather forecast even for short time intervals (say, two-weeks in advance). We will also discuss soliton waves, so that we can explain the nature of tsunami waves.
McMaster University, GS/102

7 MARCH 2006	Studying Math and Careers in Math
12:30-1:20pm	[Math Day - activities for high school students] Presentation, and question-and-swer session on university mathematics and careers in mathematics.
McMaster University, HH302

4 MARCH 2006	We Don't Need No Education ...
9:40-10:50am	[Global Citizenship Conference] Critical examination of the role and purpose of education (mathematics, science, and, in general) in today's global society. Education as commodity. Education as a basic human right ­ success or failure? Is education for all really education for all? When we implement no-child-left-behind type of policy in education, who gets left behind? Information management versus knowledge ­ which is better, which is relevant? Education as a mechanism of power and control.
McMaster University, in MDCL building

4 MARCH 2006	... As a Matter of Fact, Math is Fun
2-4pm	[Mac Cafe Scientifique Series for students grades 7-12] EVERYONE WELCOME! Variety of fun math activities, showing how math is important, relevant, and - not difficult to do. What is special about social insurance numbers and credit cards? Crossing a bridge and counting cannonballs. What can four fours do? Rabbits and the End fo the World puzzle. Also a 30-minute lecture on what math is good for, and stories about what mathematicians do these days. Have a look at sample activities
Chapters Bookstore, Ancaster

13 FEBRUARY 2006	Space and Dimension
9:30am-10:20am	[Origins Seminar. ORIGINS 2S03] What does the space that surrounds us look like? Are we able to see it, feel it, touch it? Is it finite or infinite? We do not pretend to know the answers. But we propose to examine several case studies that will help us understand things a bit better. What is the shortest path between two points in space? How would our mundane three-dimensional existence change if we were suddenly pulled into the fourth dimension? Concept of the space-time and metric. How do mathematicians describe black holes? We will develop a reasonable scenario for time travel into the future.
McMaster University, location: LSB B130A

9 FEBRUARY 2006	How Did Gauss Learn Math?
12:30-1:20pm	[Math and Society; Thematic Thursdays series of lectures] Interesting facts, stories on historic development of teaching and learning mathematics in various cultures.
GS/102

28 JANUARY 2006	Mathematics and Media
10am-2pm	[session of the Ontario Mathermatics Education Forum] Discussion on numerous aspects and issues related to presentation of mathematics in media and in popular culture.
Fields Institute, Toronto

26 JANUARY 2006	Dynamics of Cancer Growth
12:30-1:20pm	[Thematic Thursdays series; Guest: Richard Butler, McMaster University] In our math course, we developed an exponential growth model for cancer cells. How realistic is the model, i.e., how well does it describe the real growth of a cancer? What aspects of cancer growth are not included in the model? How can the model be adjusted to account for these?
McMaster University, GS/102

22 JANUARY 2006	Infinity: the Most Fascinating of all Ideas (view presentation)
3:00pm	[Royal Canadian Institute Sunday Science Lecture] Infinity has many faces. Sometimes, we perceive it as a "number" larger than all numbers. For indigenous people of Australia and New Guinea, infinity begins at seven. For the Moors - creators of exquisite mosaics and patterns whose sophistication has never been surpassed - infinity was a repetition of a single artistic motif. Infinity is eternity, divinity, love, madness ... In this lecture, I will touch upon many amazing aspects of infinity. I will explain straightforward concepts, developed by mathematician Georg Cantor, that form the basis of our modern understanding of infinity. Cantor had the courage to look infinity into its eyes - and what he saw deeply shocked him. 'I see it, but I do not believe it,' he exclaimed as he witnessed his discoveries, unleashed, shaking mathematics to its core and changing it forever. Cantor died in a mental institution. What drove him to insanity? Does infinity really exist? If so, where can we find it? Is our universe large enough to encompass infinity?
J.J.R. Macleod Auditorium, Medical Sciences Building, University of Toronto, 1 King's College Circle, Toronto

PAST PRESENTATIONS (2005)

6 DECEMBER 2005	Mathematics and Beauty in Islamic Architecture
12noon-1pm	[University of Toronto - Mississauga University Lecture Series] There is much to see and admire in the Alhambra Palace (Granada, Spain): exquisite rooms, decorated with stone and wood carvings, finest ornaments, and calligraphy; night sky represented in ceilings built of thousands of pieces of wood; gardens, courtyards and fountains; monuments, towers, archways - the list is endless. Quite possibly, an immense wealth of ornamental patterns, friezes, mosaics, star designs, and brickwork motifs tops the list. Among those, mosaics are perhaps the most interesting and the most intriguing. Scientists and artists working in the Islamic world pushed geometry to its limits, creating patterns and configurations whose sophistication has never been surpassed. Investigating numerous possibilities, based on experience and long tradition, builders of mosaics in the Alhambra created them all in the sense of the mathematics theorem on the classification of plane crystallographic groups (or wallpaper patterns). Mosaics are an invitation for a 'dynamic' experience, different from enjoying a picture of a landscape. Our eye is not able to focus on one location; there is no centre, no boundary and no preferred direction. This presentation suggests the use of a vocabulary from geometry to express some of our visual experiences.
Mississauga Central Library, 301 Burnhamthorpe Road W, Mississauga

30 NOVEMBER 2005	Infinity: the Most Fascinating of all Ideas
12noon-1pm	[University of Toronto - Oakville University Lecture Series] Infinity has many faces. Sometimes, we perceive it as a "number" larger than all numbers. For indigenous people of Australia and New Guinea, infinity begins at seven. For the Moors - creators of exquisite mosaics and patterns whose sophistication has never been surpassed - infinity was a repetition of a single artistic motif. Infinity is eternity, divinity, love, madness ... In this lecture, I will touch upon many amazing aspects of infinity. I will explain straightforward concepts, developed by mathematician Georg Cantor, that form the basis of our modern understanding of infinity. Cantor had the courage to look infinity into its eyes - and what he saw deeply shocked him. 'I see it, but I do not believe it,' he exclaimed as he witnessed his discoveries, unleashed, shaking mathematics to its core and changing it forever. Cantor died in a mental institution. What drove him to insanity? Does infinity really exist? If so, where can we find it? Is our universe large enough to encompass infinity?
Oakville Public Library, 120 Navy Street, Oakville

28 NOVEMBER 2005	Art, Architecture and Mathematics
9:30-11am	[High School Mathematics Presentation] Mathematics (and sciences in general) have always been a source of inspiration to artists and architects. The direction also reverses ... ideas that first appeared in literature, or art, later found their way into physics and mathematics theories (for instance, the question about existence of parallel realities/universes has been raised many centuries ago!). We will explore several case studies. Concepts of space-time and fourth dimension found their way into art (Picasso, Braque, Dali), and architecture (Arc de la Defense in Paris). Ndebele African art patterns reveal sophisticated symmetric patterns. Architects use geometry in design (Bilbao Guggenheim Museum, Esplanade Performing Arts Centre in Singapore and Sydney Opera House).
Lecture Hall, Cardinal Newman Secondary School, 127 Gray Rd. Stoney Creek

22-26 NOVEMBER 2005	Suggestion For A Theoretical Model For Secondary-Tertiary Transition In Mathematics
tba	[Kingfisher Delta 2005 - The Fifth Southern Hemisphere Symposium on Undergraduate Mathematics and Statistics Teaching and Learning - presentation, with Megan Clark] Abstract: The transition ('gap') between secondary and tertiary education in mathematics is a complex phenomenon covering a vast array of problems and issues. Although there is evidence of similar gaps in other disciplines in science and beyond, it seems that the transition in mathematics is by far the most serious and the most problematic. Based on certain anthropological notions, we suggest a model for the secondary-tertiary transition in mathematics. Although we focus on the area of mathematics, and on transition between a secondary institution and university (and, to a lesser degree, college), the model could be applied, with minor modifications, not only to other transitions in mathematics (primary-middle, primary-secondary, etc.) but to other areas as well. This model provides a useful lens through which we can examine the process of transition from secondary to tertiary mathematics, and also offer ways of improving present strategies and suggest new ones.
Fraser Island, Queensland, Australia

16 NOVEMBER 2005	What is New in Mathematics?
5-6pm	[Presentation for high school students] Abstract: Case studies of present-day research afforts in mathematics, including error correcting codes and computer security, data compression and transmission of large amounts of data; also, some (presently) unsolved problems in mathematics
McMaster University, HH/312

10 NOVEMBER 2005	Social and Cultural Issues in Teaching Mathematics
12:30-1:20pm	[Thematic Thursdays Lecture Series] We plan to discuss ways in which mathematics is taught on all levels, from elementary to tertiary. Case studies of math education among Canadian Inuit and Maori (New Zealand) will be presented.
McMaster University, GS-102

26 OCTOBER 2005	Mysteries of Infinity
3:45pm-4:45pm	[Lecture for high school students - same topic as the public lecture scheduled for 19 October] Infinity has many faces. Sometimes, we perceive it as a "number" larger than all numbers. For indigenous people of Australia and New Guinea, infinity begins at seven. For the Moors - creators of exquisite mosaics and patterns whose sophistication has never been surpassed - infinity was a repetition of a single artistic motif. Infinity is eternity, divinity, love, madness ... In this lecture, I will touch upon many amazing aspects of infinity. I will explain straightforward concepts, developed by mathematician Georg Cantor, that form the basis of our modern understanding of infinity. Cantor had the courage to look infinity into its eyes - and what he saw deeply shocked him. 'I see it, but I do not believe it,' he exclaimed as he witnessed his discoveries, unleashed, shaking mathematics to its core and changing it forever. Cantor died in a mental institution. What drove him to insanity? Does infinity really exist? If so, where can we find it? Is our universe large enough to encompass infinity? Could our space have infinitely many dimensions?
Columbia International College

20 OCTOBER 2005	Math for the Universe
10:30pm - 11:20pm	[Engineering and Science Olympics] What does the space that surrounds us look like? Are we able to see it, feel it, touch it? Is it finite or infinite? We do not pretend to know the answers. But we propose to examine several case studies that will help us understand things a bit better. What is the shortest path between two points in space? How would our mundane three-dimensional existence change if we were suddenly pulled into the fourth dimension? Concept of the space-time and metric. How do mathematicians describe black holes? We will develop a reasonable scenario for time travel into the future.
McMaster University, MDCL 1008

19 OCTOBER 2005	Mysteries of Inifinty
6:30-7:30pm	[Public Lecture] Infinity has many faces. Sometimes, we perceive it as a "number" larger than all numbers. For indigenous people of Australia and New Guinea, infinity begins at seven. For the Moors - creators of exquisite mosaics and patterns whose sophistication has never been surpassed - infinity was a repetition of a single artistic motif. Infinity is eternity, divinity, love, madness ... In this lecture, I will touch upon many amazing aspects of infinity. I will explain straightforward concepts, developed by mathematician Georg Cantor, that form the basis of our modern understanding of infinity. Cantor had the courage to look infinity into its eyes - and what he saw deeply shocked him. 'I see it, but I do not believe it,' he exclaimed as he witnessed his discoveries, unleashed, shaking mathematics to its core and changing it forever. Cantor died in a mental institution. What drove him to insanity? Does infinity really exist? If so, where can we find it? Is our universe large enough to encompass infinity? Could our space have infinitely many dimensions?
McMaster University, JHE 264

13 OCTOBER 2005	Aardvarks and Titanium Junkyards
12:30-1:20pm	[Thematic Thursdays in Arts and Science Series Lecture] Mathematics has always been an inexhaustible source of inspiration to artists and architects. Case studies of cubism, and Ndebele African art patterns. Also, Bilbao Guggenheim Museum, Esplanade Performing Arts Centre in Singapore and Sydney Opera House.
McMaster University, GS-102

29 SEPTEMBER 2005	Concept of Dimension
1:30pm - 2:20pm	[Science 2B3 (Big Questions) Guest Lecture] Concept of a spatial dimension. Developing ways of thinking about fourth, fifth and higher dimensions. Case studies of transition from lower to higher dimensions.
McMaster University, CNH/104

29 SEPTEMBER 2005	Error-detecting and Error-correcting Codes, Security
12:30-1:20pm	[Arts and Science Applications of Math Series] Introduction to error-detecting and error-correcting codes, with applications (such as writing information on a music CD or on a DVD). Issues of security of information transmitted over internet. Introduction to data compression.
McMaster University, GS-102

26 SEPTEMBER 2005	Modern Mathematics: Present-Day Applications
9:30-11am	[Presentation for high school students] Abstract: Case studies of present-day research afforts in mathematics: error correcting codes and computer security, data compression and transmission of large amounts of data; weather forecasting and understanding disasters (tsunami); also, mention of some (presently) unsolved problems in mathematics
St Mary's Catholic Secondary School, Hamilton

22 SEPTEMBER 2005	Art of Teaching Problem-Solving
6-7pm FULL	[BHSc Outreach program] Abstract: Discussion of techniques and strategies of problem-solving in mathematics. Presentation and communication skills.
McMaster University, MDCL 3023

15 SEPTEMBER 2005	What 's Going on in Math These Days?
12:30-1:20pm	[Arts and Science Thematic Thursdays Series] Applications of Math, First Lecture ... Besides drinking coffee, what do mathematicians do these days? We'll look at case studies of modern research efforts in mathematics: including error correcting codes and computer security, data compression and transmission of large amounts of data.
GS-102

11-19 JULY 2005	Mathematics and Its Applications
.	[SHAD VALLEY 2005 Math Program] Series of five presentations on mathematics and its applications. Plus, a lecture and workshop on building geodesic domes.
Hamilton Hall, McMaster University

23 JUNE 2005	"Learning How to Teach and Learn Mathematics: 'Teaching Mathematics' Course at McMaster University"
.	[1st Africa Regional Congress of the International Commission on Mathematical Instruction ] The course "Teaching Mathematics" has been designed in an attempt to improve the quality of instruction delivered by undergraduate teaching assistants in mathematics at McMaster University. Problems traditionally experienced by our teaching assistants range from a lack of knowledge of mathematics content, and lack of guidance by lecturers and course coordinators, to rudimentary teaching skills without opportunities for improvement, to low motivation, and inadequate preparation for a tutorial session. A group of undergraduate students are enrolled in the "Teaching Mathematics" course and concurrently work as teaching assistants for a first-year calculus course. In other words, they are both teachers and learners at the same time. A framework for the "Teaching Mathematics" project is that of a learning partnership on several levels: partnership between undergraduate students, i.e., between undergraduate teaching assistants, and between undergraduate teaching assistants and students in their tutorial groups. It is also a learning partnership between the "Teaching Mathematics" course instructor and the students (in the "Teaching Mathematics" course). Such framework is an echo of the fact that education must be an active and inspired two-way communication. In this session, I plan to outline the design of the "Teaching Mathematics" course, and to discuss various issues related to both the course and to my students' performance as teaching assistants. Teaching assistants work on improving their written and oral communications skills through writing about mathematics, conducting tutorial sessions and through one-on-one sessions with their students during office hours. In "Teaching Mathematics" sessions, we discuss and analyze elements that constitute good teaching practice - especially preparation (knowledge of mathematics) and communication. By reading and criticizing journal and newspaper articles and books we get introduced to theoretical aspects of teaching, and, in particular, teaching mathematics. By learning how to teach mathematics we also learn how to learn mathematics - certainly, a very valuable asset - especially for those students who plan to major in mathematics. "Teaching Mathematics" course provided me with an opportunity to constantly monitor the work of my students - my teaching assistants (we used evaluations, self-evaluations and personal interviews). I have collected valuable data and information that I plan to discuss in my session.
University of the Witwatersrand, Johannesburg, South Africa

23 JUNE 2005	"Mathematics Background Survey ­ An Insight Into Students' Preparation for University Mathematics Courses"
.	[1st Africa Regional Congress of the International Commission on Mathematical Instruction ] Transition between secondary and tertiary education in mathematics is a complex phenomenon covering a vast array of problems and issues. Although there is evidence of existence of similar issues in other disciplines in science and beyond, it seems that the transition in mathematics is by far the most serious and the most problematic. In spite of all efforts and energy ventured into the pre-tertiary mathematics education, the knowledge and skills of incoming university students are far from satisfactory. Students coming to tertiary institutions are more numerous and more diverse; they have different and often unclear views of mathematics and its role in their future career. Their views echo a seemingly contradictory (but, unfortunately, true) fact that, although the importance of acquiring mathematical skills has been rising, the lack of appreciation of mathematics on the part of the public is evident. Curricular changes may also have influenced characteristics of incoming students. University teachers may largely be unaware of or unwilling to accept the magnitude of these changes. Moreover, the amount of research on mathematics education at the tertiary level is still modest. Inquiry into both social and cognitive backgrounds of students may provide an insight into how the two factors relate to and affect one another. The aim of this talk is to present partial results of a survey ('Mathematics Background Survey') of incoming university students (future majors in science), that has been conducted at McMaster University since 2001. The survey has two parts, roughly described as 'narrative' and 'mathematics.' Besides inquiring about basic demographic data, the 'narrative' part asks students to describe their experiences with high school mathematics and their expectations about the university mathematics courses. The 'mathematics' part aims to identify students' strengths and weaknesses in the number of areas that are essential for their success in university mathematics courses. Information on students' experiences with mathematics in high school is being examined for correlations with their success in their first-year mathematics course. Information on students' background preparation and experience in mathematics should be very valuable to university faculty, some of whom are not aware of the magnitude of changes in the incoming student population.
University of the Witwatersrand, Johannesburg, South Africa

8-11 JUNE 2005	ratemyprof.com (HAD TO CANCEL)
TBA	[STLHE 2005 Conference] Unconventional way to find my students' voices? ... Internet, of course! About a year ago, I visited the site www.ratemyprofessors.ca. Needless to say, I have become one of the regulars, reading not just my comments, but also those of my colleagues. So, what have I learnt? Well ... much more than I expected.
University of PEI, Charlottetown, PEI

28 MAY 2005	"Mathematics and Beauty in Islamic Architecture"
11am-noon	[Subtle Technologies Conference 27-29 May] There is much to see and admire in the Alhambra Palace: exquisite rooms, decorated with stone and wood carvings, finest ornaments, and calligraphy; night sky represented in ceilings built of thousands of pieces of wood; gardens, courtyards and fountains; monuments, towers, archways - the list is endless. Quite possibly, an immense wealth of ornamental patterns, friezes, mosaics, star designs, and brickwork motifs tops the list. Among those, mosaics are perhaps the most interesting and the most intriguing. Scientists and artists working in the Islamic world pushed geometry to its limits, creating patterns and configurations whose sophistication has never been surpassed. Investigating numerous possibilities, based on experience and long tradition, builders of mosaics in the Alhambra created them all ? in the sense of the mathematics theorem on the classification of plane crystallographic groups (or wallpaper patterns). Mosaics are an invitation for a 'dynamic' experience, different from enjoying a picture of a landscape. Our eye is not able to focus on one location; there is no centre, no boundary and no preferred direction. This presentation suggests the use of a vocabulary from geometry to express some of our visual experiences.
Innis Townhall, 2 Sussex Avenue (at St. George) University of Toronto campus

20 MAY 2005	Narratives In Mathematics - Case Of Arts and Science Mathematics Course at McMaster University
1:00pm	[First International Symposium on Mathematics and Its Connections to the Arts and Sciences 19-21 May 2005] Interdisciplinary component of the Mathematics course taught in the Arts and Science Programme at McMaster University is implemented in several ways, varying in depth, width and level of involvement of other courses. Of a number of issues related to the course, this paper uses instructors' experience and examples of students' writing to discuss the features of the narrative in mathematics. Used as a vehicle to enhance understanding of mathematics and to build and improve research and communication skills, good writing is a key to a successful and productive interdisciplinary mathematics course.
The University of Education, Schwäbisch Gmünd, Germany

13 MAY 2005	"Infinity - the Most Fascinating of All Ideas"
1:30-2:30pm	[McMaster Accelerated Students Workshop] Infinity has many faces. Sometimes, we perceive it as a number larger than all numbers. For indigenous people of Australia and New Guinea, infinity begins at six. For the Moors - creators of the most beautiful mosaics the world has ever seen - infinity was in a repetition of a single artistic motif. Infinity is eternity, divinity, love, death ... Modern mathematicians have embraced infinity as one embraces a good friend; but a few have contemplated suicide rather than being forced to face it. Georg Cantor, early explorer of infinity, died in a mental institution. What exactly drove him to insanity? Does infinity really exist? If so, what is it? Where can we find it? Is our universe large enough to encompass infinity?
McMaster University, TBA

6 MAY 2005	Learning how to Teach and Learn Mathematics: "Teaching Mathematics" Course at McMaster University
2:00pm-3:30pm	[Canadian Mathematics Education Forum 2005 5-7 May 2005] I plan to briefly outline the design of the "Teaching Mathematics" course, and to discuss various issues related to both the course and to students' performance as teaching assistants. "Teaching Mathematics" course provided me with an opportunity to constantly monitor the work of my teaching assistants (we used evaluations, self-evaluations and personal interviews). I have collected valuable data and information that I plan to present. (Full-length abstract from the Forum website)
University of Toronto

31 MARCH 2005	"Using Undergraduate TAs in Large and Online Classes"
2:30pm-4:30pm	[CLL Seminar, Dick Day, McMaster University; Arshad Ahmad, Concordia University, Miroslav Lovric, McMaster University] We all have concerns about large classes and inadequate teaching resources, but we underutilize one of our most valuable teaching resources: our own undergraduates. Experience with undergraduate TAs at McMaster suggests both that undergraduate TAs bring a number of important advantages to the classroom, and that they count their teaching experience as one of the most valuable aspects of their own education. Dick will be describing some of his experiences with undergraduate TAs. Arshad's experience with an elective course on Personal Finance at Concordia University has been focused on the model of distributed expertise and multiple tools for learning. This course has grown into one of the largest in Canada, and enjoys very low attrition rates for one important reason: The TA's. Their vital role, motivation to continue and input in continuous development will be highlighted. Miroslav has learned a great deal about undergraduate teachers from teaching his "Teaching Mathematics" course, and has gained valuable insights from a variety of sources. Recently, the Department promoted a few of their most successful TAs into 'Head TAs,' giving them additional duties and more responsibility. How are they coping with the challenges their new job presents? In the past several years, we have witnessed an increase in a number of students interested in teaching careers. Their undergraduate teaching jobs provide them with a set of skills that will help them both in their studies and later, when they start teaching in high school or in university.
McMaster University, MDCL 3022

17 MARCH 2005	"Nothing Really Matters"
12:30-1:20pm	[Thematic Thursdays series; Guest: John Browning, McMaster University] Conversation about zero, emptiness, void, vacuum, nonexistence, and other related nothings.
McMaster University, GS/101

7 MARCH 2005	"Symmetry"
11:00-12:30	[Math Day, with Deirdre Haskell] Exploration of symmetric patterns and introduction to mathematical concept of summetry and group.
McMaster University, CIBC Banquet Hall in Student Centre

3 MARCH 2005	"Titanium Junkyards and Copulating Aardvarks"
8:30-9:20am	[Thematic Thursdays series] Mathematics has always been an inexhaustible source of inspiration to artists and architects. Case studies of cubism, and Ndebele African art patterns. Also, Bilbao Guggenheim Museum, Esplanade Performing Arts Centre in Singapore and Sydney Opera House.
McMaster University, HH/104

2 MARCH 2005	"Can Mathematics Predict the Weather?"
4:30-5:30pm	[Math@Mac presentation for high school students;] In this lecture we will discuss mathematical models that are used in weather forecasting. Analysis of such models will lead us to the concept of chaotic behaviour. We will try to understand why is it not possible to calculate accurately a weather forecast even for short time intervals (say, two-weeks in advance). We will also discuss soliton waves, so that we can explain the nature of tsunami waves.
McMaster University, Hamilton Hall 305

1 MARCH 2005	"Transition, A Dialogue"
4:30-6pm FULL	Dialogue with high school teachers on issues of transition between secondary and tertiary mathematics education.
McMaster University, Hamilton Hall 305

26 FEBRUARY 2005	"Double Cohort, Fall 2004, Preliminary Report"
10am-2pm	[Ontario Math Education Forum meeting] Presentation and discussion of issues related to the Double Cohort; analysis of performance of first-year students in calculus courses at McMaster University.
Fields Institute, Toronto

18 FEBRUARY 2005	"Mathematics in Applications"
8:30-9:20am	[Arts and Science Math series] Second in the series on applications of mathematics, this lecture will discuss soliton waves (tsunamis) and logistic growth in the case of a spread of an infectuous disease.
McMaster University, HH/104

9 FEBRUARY 2005	"Do You Know How to Add Numbers?"
4:30-5:30pm	[Math@Mac presentation for high school students] We can easily add two numbers; computers can add billion numbers is less than a second. But how about adding an infinite number of numbers? Mathematicians have thought about it for more than thousand years, and have come up with the concept of an infinite series. We will investigate various strategies (both algebraic and geometric), and will obtain a number of amazing results.
McMaster University, Hamilton Hall 305

27 JANUARY 2005	"Science and Society"
12:30-1:20pm	[Thematic Thursdays series. Guest: Shawn Loewen, McMaster University] Popular myths about science or mathematics; competing histories of the origins and/or models of the development of science or mathematics. Science/mathematics as an authoritative & powerful institution controlling knowledge production. Is science value-free?
McMaster University, GS/101

13 JANUARY 2005	"Dynamics of Cancer Growth"
12:30-1:20pm	[Thematic Thursdays serie. Guest: Richard Butler, McMaster University] In our math course, we developed an exponential growth model for cancer cells. How realistic is the model, i.e., how well does it describe the real growth of a cancer? What aspects of cancer growth are not included in the model? How can the model be adjusted to account for these?
McMaster University, GS/101

PAST PRESENTATIONS (2004)

15 DECEMBER 2004	"Exploring Symmetry IV"
4:30-5:30pm	[Math@Mac presentation for high school students] This is the last in a series of presentations/ workshops that will explore various aspects of symmetry: from its occurence in nature, art, and architecture, to its mathematical foundations (concept of a group). In this lecture we will explore cyclic and dihedral groups.
McMaster University, Hamilton Hall 312

2 DECEMBER 2004	"What's Going on in Math These Days"
12:30-1:20pm	[Thematic Thursdays series; for list of upcoming sessions,] Besides drinking coffee, what do mathematicians do these days? We'll look at case studies of modern research efforts in mathematics: error correcting codes and computer security, data compression and transmission of large amounts of data; some (presently) unsolved problems in mathematics and their relevance.
McMaster University, KTH/B132

1 DECEMBER 2004	"Exploring Symmetry III"
4:30-5:30pm	[Math@Mac presentation for high school students] This is the third in a series of presentations/ workshops that will explore various aspects of symmetry: from its occurence in nature, art, and architecture, to its mathematical foundations (concept of a group). In this lecture we will discuss further the mathematical concept of a group.
McMaster University, Hamilton Hall 312

29 NOVEMBER 2004	"What do Mathematicians do These Days?"
9:00-10:00am FULL	[Presentation for high school students] Abstract: Case studies of present-day research afforts in mathematics: error correcting codes and computer security, data compression and transmission of large amounts of data; (presently) unsolved problems in mathematics
St Mary's Catholic Secondary School, Hamilton

18 NOVEMBER 2004	"Teaching Mathematics: Canadian Experience"
12:30-1:20pm	[Thematic Thursdays series] Guest: Megan Clark, University of Wellington, New Zealand Case study of math education among Canadian Inuit and Indigeneous People.
KTH/B132

17 NOVEMBER 2004	"Exploring Symmetry II"
4:30-5:30pm	[Math@Mac presentation for high school students] This is the second in a series of presentations/ workshops that will explore various aspects of symmetry: from its occurence in nature, art, and architecture, to its mathematical foundations (concept of a group). In this lecture we will define the concept of a group and will investigate occurence of symmetry in nature.
McMaster University, Hamilton Hall 312

4 NOVEMBER 2004	"Social and Cultural Issues in Teaching Mathematics"
12:30-1:20pm	[Thematic Thursdays series] Guest: Megan Clark, University of Wellington, New Zealand We plan to discuss ways in which mathematics is taught on all levels, from elementary to tertiary. Case studies of math education among Canadian Inuit and Maori (New Zealand) will be presented.
KTH/B132

3 NOVEMBER 2004	"Mathematics of Communication and Decision-Making in Medicine"
7:00pm-8:00pm	[Public lecture] An increasing amount of data that we encounter (not only in medicine) comes in formats that are mathematical in nature: numeric data; visual information in the form of graphs, charts and diagrams; uncertainly, expressed as percent or chance, to mention a few. How do we make sense of it? In this talk I will explore case studies that will illustrate how basic concepts from mathematics appear in a variety of areas in health sciences. I will convince you that, in order to make sense of the data that you (will) inevitably encounter on a daily basis, you need to understand basic math really well. Only when you understand all aspects of the case you are dealing with, you will be able to communicate your ideas and thoughts effectively to your colleagues and peers. Significant aspect of your job as a health care worker/physician/etc. will be/is communication with your patients. What you say - and how you say it - could make a big difference to them. This might be your most important math lecture! Although no mathematics prerequisite is needed, it will help a bit if you remember a few things from calculus, such as exponential growth and decay.
McMaster University, Burke Science Building 147

3 NOVEMBER 2004	"Exploring Symmetry"
4:30-5:30pm	[Math@Mac presentation for high school students] This is the first in a series of presentations/ workshops that will explore various aspects of symmetry: from its occurence in nature, art, and architecture, to its mathematical foundations (concept of a group). In this lecture we will investigate so-called point groups.
McMaster University, Hamilton Hall 312

23 OCTOBER 2004	"Transition from Secondary to Post-Secondary Mathematics: Changing Features of Students' Mathematical Knowledge and Skills and Their Influence on Students' Success"
3:50-4:30pm	[PME-NA CONFERENCE (Psychology of Mathematics Education - North America) - with Ann Kajander, Lakehead University] Abstract: This study explores the changes in knowledge of certain areas of mathematics and various skill levels of students entering first year mathematics courses, and examines their relationship to students' success in first-year university mathematics courses. Of particular interest to us are students who appear to enter university mathematics courses with low technical skills in mathematics, yet recover quickly and are successful. This exploratory study examines data collected over a three-year period from students in both the 'old' and 'new' Ontario curricula. The main focus of the current report is the difference between the incoming knowledge and skills and the performance in the first year mathematics course of these two groups of students.
Windsor Room, Delta Chelsea Hotel, Toronto

21 OCTOBER 2004	"Mathematics Research Today"
2:30-3:20 pm	[Engineering and Science Olympics lecture] Abstract: Today, millions of bits of sensitive and confidential information need to be sent over computers daily. In order to ensure security, the information must be coded ­ hence the permanent need for secure, hard-to-break codes. Presently accepted standard, the so-called RSA encryption code uses modular arithmetics. Learning how the information is coded will help us understand why is the code so hard to break. Next, we learn about error-detecting and error-correcting codes. After presenting basics, we will explore how information is coded onto music and video disks (CD, DVD). As another application of modular arithmetics, we will explore the way colour works in computers. If time permits, we will discuss mathematics of data compression, in particular the way it is applied to storing millions of cards with fingerprints. Finally, at the end of the lecture we will mention Goldbach's conjecture, an old, but still unsolved mathematics problem.
McMaster University, Hamilton Hall 104

21 OCTOBER 2004	"Assessing Students"
12:30-1:20 pm	[Centre for Leadership in Learning Networking Luncheon Discussion] Abstract: Two experienced faculty members (Miroslav Lovric and ??), and CLL staff will launch a discussion and help answer your questions such as: - What is the right balance of tests and assignments? - Many students did poorly (or too well) on a test, what can I do? - How do I deal with complaints about grading? - How do I determine students prior knowledge? - How do I set student standards?
McMaster University, General Science 217

20 OCTOBER 2004	"Art of Teaching Problem-Solving"
5:30-6:20 pm FULL	Abstract: Discussion of techniques and strategies of problem-solving in mathematics. Presentation and communication skills.
McMaster University, MDCL 3024

20 OCTOBER 2004	"FBI Fingerprint Image Compression Standard"
4:30-5:20pm LIMITED SPACE	[Public lecture in the lecture series for high school students] Abstract: We will outline how mathematics (wavelets) is used to compress large amounts of data on fingerprint cards, for storage and electronic transmission.
McMaster University, Hamilton Hall 312

24 SEPTEMBER 2004	"Concept of a Dimension"
2:30pm - 3:30pm	SCIENCE 2B3 (BIG QUESTIONS) GUEST LECTURE Concept of a spatial dimension. Developing ways of thinking about fourth, fifth and higher dimensions. Case studies of transition from lower to higher dimensions.
McMaster University MDCL-1105

4-11 JULY 2004	ICME-10 Conference
.	ICME-10 CONFERENCE (need details) presentation in Topic Study Group 3; presentation in Discussion Group 21, Sharing Experience group leader
Copenhagen, Denmark

30 MARCH 2004	"Mountains or Molehills?" (Large Classes Panel) with Arshad Ahmad (Concordia U) and Dick Day (McMaster)
2:00pm-3:00pm	Ontario's double cohort arrived at university last year, higher university enrolments are predicted for the next few years, and many instructors find themselves dealing with much larger classes than they are used to. This session will give participants opportunities to discuss their concerns about (and solutions for) large class challenges and interact with a panel of instructors with many years of experience dealing with large classes."
McMaster University Student Centre, Room 224

12, 19 and 26 MARCH 2004	"Mathematics in Communication in Medicine"
2:30pm-4:20pm FULL	Case studies of communication of mathematical information in contexts related to medicine. (BHSc 4U6 guest lectures)
McMaster University, GS 218

11 MARCH 2004	"Mathematics of Communication and Decision-Making in Medicine"
7:00pm-8:00pm	An increasing amount of data that we encounter (not only in medicine) comes in formats that are mathematical in nature: numeric data; visual information in the form of graphs, charts and diagrams; uncertainly, expressed as percent or chance, to mention a few. How do we make sense of it? In this talk I will explore case studies that will illustrate how basic concepts from mathematics appear in a variety of areas in medicine. I will convince you that, in order to make sense of the data that you (will) inevitably encounter on a daily basis, you need to understand basic math really well. Only when you understand all aspects of the case you are dealing with, you will be able to communicate your ideas and thoughts effectively to your colleagues and peers. A significant aspect of your job will be/is communication with your patients. What you say - and how you say it - could make a big difference to them. This might be your most important math lecture. (Although no mathematics prerequisite is needed, it will help a bit if you remember a few things from calculus, such as exponential growth and decay.)
McMaster University, Chester New Hall 104

9 MARCH 2004	" ... Hold Infinity in the Palm of Your Hand, and Eternity in an Hour" (Science in the City lecture series)
7:00pm-8:00pm	Infinity has many faces. Sometimes, we perceive it as a "number" larger than all numbers. For indigenous people of Australia and New Guinea, infinity begins at seven. Infinity for Van Gogh was a vast, unending plane, on which imagination is given free rein. For the Moors - creators of exquisite mosaics and patterns whose sophistication has never been surpassed - infinity was a repetition of a single artistic motif. Infinity is eternity, divinity, love, madness ... In this lecture, I plan to present a sketch of a cultural history of infinity, spanning thousands of years. I will explain amazingly straightforward concepts, developed by mathematician Georg Cantor, that form the basis of our modern understanding of infinity. Cantor had the courage to look infinity into its eyes - and what he saw deeply shocked him. 'I see it, but I do not believe it,' he exclaimed as he witnessed his discoveries, unleashed, shaking mathematics to its core and changing it forever. Cantor died in a mental institution. What drove him to insanity? Does infinity really exist? If so, where can we find it? Is our universe large enough to encompass infinity? Although no mathematics background is required, certain amount of courage is expected from those in attendance. This lecture might threaten, and possibly change, some of our most cherished notions about life and the world we live in. It might take all of eternity to reach infinity. But sometimes, infinity gets so close to us, that, as if in a dream, we feel that we can hold it in the palm of our hand.
Hamilton Spectator Auditorium, 44 Frid Street, Hamilton   Doors open at 6:30pm Lecture begins at 7pm Lecture will be followed by a question- and- answer session Light refreshments will be available

1 MARCH 2004	"When Size Matters"
12:00noon- 2:00pm	With an increase in class size, virtually all aspects of teaching - from pedagogical decisions about the material that needs to be covered, to designing effective small-class tutorials, to discipline and student motivation issues - change in a fundamental way, introducing a number of new problems and challenges. In this presentation I plan to focus on specific strategies that we have been implementing in an effort to improve quality of teaching in our large classes.
University of Toronto at Scarborough

27 FEBRUARY 2004	"Jumping over Fire: Some Hot Issues in the Transition from Secondary to Tertiary Education"
12:00noon-1:00pm	The 'gap' between the secondary and the tertiary education in mathematics is a complex phenomenon covering a vast array of issues. Rather than speaking in general terms, I plan to focus on specific problems that we (at McMaster University) have encountered, and on our attempts at dealing with them. I will report on the joint work with Ann Kajander (Lakehead University), on our study of the Mathematics Background Questionnaire. Besides getting a fairly decent snapshot of mathematics knowledge, the survey provided us with valuable information on our students' high school experiences and expectations of their university mathematics courses. Moreover, I will talk about the project 'Transition from secondary to tertiary education in mathematics - strategies that work' that we have been involved with. This project deals with the transition issues in a more global context.
OAME Conference, Thunder Bay

26 FEBRUARY 2004	"Smart Numbers" (Fireball Show for high school students)
11:00-11:30am FULL	You bought a phone card, and are making a phone call: dial the number, and punch in the card number. The voice on the other side tell you that the card number you entered is incorrect. Then you realized that you indeed made a mistake - you switched the last two digits. How did they know? Your CD produces a prefect sound even though your cat just walked over it, its feet wet and muddy ... A brief introduction into the exciting world of error-correcting codes.
CIBC Hall, MUSC, McMaster University

24 JANUARY 2004	"OAC vs Grade 12: Anything New and Exciting?"
10am-2pm	Preliminary report on issues related to the double cohort in first-year mathematics courses at McMaster University. Mathematics background survey results (the survey was conducted in early September 2003) will be related to the in-class and final performance of students in the first-year calculus course for science students.
Mathematics Education Forum, Fields Institute, Toronto

PAST PRESENTATIONS (FALL 2003)

4 DECEMBER 2003	"Convergence of Media: Textbooks and Internet - What's the Difference?"
10:30am-11:00am	I plan to report on my initial investigation into the most recent evolution of textbooks. Although I plan to present a case study of textbooks in mathematics, my discussion will cross the border into other areas. By contrasting old and new textbooks, and by comparing new textbooks to Internet sites that offer instruction, valuable conclusions on present trends in learning can be drawn. I will argue that, by abandoning 'old' textbook style, we might be in danger of abandoning important methods and ideas on teaching and learning. The conclusion of the talk will offer a creative compromise between paper and internet.
Learning Technologies Symposium, Centre for Leadership in Learning McMaster University BSB/137

27 NOVEMBER 2003	"Have Eyes to Wonder, But Lacks Tongues to Praise"
7:30pm-8:30pm	The aim of my presentation is to suggest a possibly new way of looking at objects of art that possess certain geometric features, and to provide a vocabulary to communicate those ideas. Based mostly, but not exclusively, on concepts from Euclidean geometry, this new vocabulary might help us verbalize why we perceive something as beautiful. Rather than replacing any part of our visual experience, geometry will help us make it richer. A case study of symmetries of mosaics from the Alhambra Palace in Granada, Spain, will be discussed. Mosaics present important clues in understanding the space we live in ... what do they tell us?
McMaster University Museum of Art

12 NOVEMBER 2003	"Where do we Really Live?"
7:00pm-8:00pm	What does the space that surrounds us look like? Are we able to see it, feel it, touch it? Is it finite or infinite? We do not pretend to know the answers. But we propose to examine several case studies that will help us understand things a bit better. What is the shortest path between two points in space? How would our mundane three-dimensional existence change if we were suddenly pulled into the fourth dimension? Do wormholes really exist? We will develop a reasonable scenario for time travel into the future.
McMaster University BSB/147

6 NOVEMBER 2003	"Life in Sixty-seventh Dimension" (Big Questions guest lecture)
10:30am-11:20am	Concept of a spatial dimension. Developing ways of thinking about fourth, fifth and higher dimensions. Case studies of transition from lower to higher dimensions.
McMaster University KTH/B135