What exactly is meant when we talk about religion in relationship to science? The meaning of the question is not self-evident because it is not at all apparent what sort of 'things' religion and science are--or if indeed it is right to speak of them as things in the first place.
Conceptual difficulties, the terms religion and science have been very useful to many people as general categories in which to put things that seem to share something called religion or something called science in common.
Background to contemporary discussions of the relation between religion and science is provided by the work of Ian G. Barbour. He proposed a widely influential typological method of modelling the relationship between religion and science. The Religion and Science: Historical and Contemporary Issues, for which he was awarded the prestigious and lucrative Templeton Prize for Progress in Religion (1999), is his most comprehensive account.
Most of Barbour work focuses on post-17th century European developments. He sees the new cultural situation created by the sort of natural scientific study associated with persons like Copernicus and Galileo, Newton and Darwin, as well as Faraday and Einstein as necessary developments, which believers of any stripe must engage with constructively.
Barbour further proposes four general ways that the study of human history shows us religion and science have related to each other:
as happens when scientific materialists and a biblical literalists are locked in the same room together.
as happens when religion is understood to relate exclusively to moral and spiritual truths and science to observable and materials truths.
as happens when specific religious teachings, like the doctrine of Creation, correspond with certain scientific assumptions, like the intelligibility of the natural order.
as happens when science--like evolutionary theory--is thought to demonstrate how God, i.e. the complex numinous unity that holds all things together, comes into existence through ever more complex physical, chemical, and biological systems.
My own objections to this kind of academic shorthand, or typological simplification, will become more clear as the class proceeds. For now, you need to be aware of Barbour's proposals because more recent scholarship on religion and science has been forced to wrestle with his work. When you read 'Religious Belief and the Natural Sciences: Mapping the Historical Landscape by John Hedley Brooke, note how he hard he works to find wiggle room in order to say to Barbour, 'Thanks, but no thanks.'